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We propose an approach to represent the second-quantized electronic Hamiltonian in a compact sum-of-products (SOP) form. The approach is based on the canonical polyadic decomposition of the original Hamiltonian projected onto the sub-Fock spaces formed by groups of spin–orbitals. The algorithm for obtaining the canonical polyadic form starts from an exact sum-of-products, which is then optimally compactified using an alternating least squares procedure. We discuss the relation of this specific SOP with related forms, namely the Tucker format and the matrix product operator often used in conjunction with matrix product states. We benchmark the method on the electronic dynamics of an excited water molecule, trans-polyenes, and the charge migration in glycine upon inner-valence ionization. The quantum dynamics are performed with the multilayer multiconfiguration time-dependent Hartree method in second quantization representation. Other methods based on tree-tensor Ansätze may profit from this general approach. [ABSTRACT FROM AUTHOR]

Semiconductor quantum dots (QDs) are one of the leading candidates for realizable qubits, as well as for many other advances in quantum computing and quantum communication. The spatial overlapping of wavefunctions describing each single electron in these nanoscale devices results in tunable spatial entanglement. In this article, we explore the case of two electrons in two-dimensional double quantum dot systems. We compute the two-particle wavefunction through a variational method combined with Hermite finite elements and study the spatial entanglement of electrons. We show that symmetry in the geometry of the double quantum dots plays a role in obtaining optimal entanglement, while a broken symmetry can lead to additional resonances in entanglement that are associated with the crossings of states. We also show that one can finely tune the level of spatial entanglement by altering the geometry of the quantum dots or by applying external fields, which corresponds to an "entanglement spectroscopy." Finally, we study how impurities in the potential profile of the QDs affect the level of entanglement. [ABSTRACT FROM AUTHOR]

We study the fuzzy spaces (as special examples of noncommutative manifolds) with their quasicoherent states in order to find their pertinent metrics. We show that they are naturally endowed with two natural 'quantum metrics' which are associated with quantum fluctuations of 'paths'. The first one provides the length the mean path whereas the second one provides the average length of the fluctuated paths. Onto the classical manifold associated with the quasicoherent state (manifold of the mean values of the coordinate observables in the state minimising their quantum uncertainties) these two metrics provides two minimising geodesic equations. Moreover, fuzzy spaces being not torsion free, we have also two different autoparallel geodesic equations associated with two different adiabatic regimes in the move of a probe onto the fuzzy space. We apply these mathematical results to quantum gravity in BFSS matrix models, and to the quantum information theory of a controlled qubit submitted to noises of a large quantum environment. [ABSTRACT FROM AUTHOR]

Classical General Relativity is a dynamical theory of spacetime metrics of Lorentzian signature. In particular the classical metric field is nowhere degenerate in spacetime. In its initial value formulation with respect to a Cauchy surface the induced metric is of Euclidian signature and nowhere degenerate on it. It is only under this assumption of non-degeneracy of the induced metric that one can derive the hypersurface deformation algebra between the initial value constraints which is absolutely transparent from the fact that the inverse of the induced metric is needed to close the algebra. This statement is independent of the density weight that one may want to equip the spatial metric with. Accordingly, the very definition of a non-anomalous representation of the hypersurface deformation algebra in quantum gravity has to address the issue of non-degeneracy of the induced metric that is needed in the classical theory. In the Hilbert space representation employed in Loop Quantum Gravity (LQG) most emphasis has been laid to define an inverse metric operator on the dense domain of spin network states although they represent induced quantum geometries which are degenerate almost everywhere. It is no surprise that demonstration of closure of the constraint algebra on this domain meets difficulties because it is a sector of the quantum theory which is classically forbidden and which lies outside the domain of definition of the classical hypersurface deformation algebra. Various suggestions for addressing the issue such as non-standard operator topologies, dual spaces (habitats) and density weights have been proposed to address this issue with respect to the quantum dynamics of LQG. In this article we summarise these developments and argue that insisting on a dense domain of non-degenerate states within the LQG representation may provide a natural resolution of the issue thereby possibly avoiding the above mentioned non-standard constructions. [ABSTRACT FROM AUTHOR]

Abstract\nRESEARCH HIGHLIGHTSThis work is focused on the synthesis of several transition metal complexes [ML(MA)], where M = Copper (II), Zinc (II), Cobalt (II) and Nickel (II), MA = maleic acid and L = Schiff base generated from benzene-1,2-diamine [o-phenylenediamine] and 4-chlorobenzaldehyde. The characterization using Fourier-Transform Infrared, Nuclear Magnetic Resonance spectroscopy, Ultraviolet-Visible spectra, Mass, Electro Paramagnetic Resonance and elemental analysis confirm the square planar geometry of the complexes. The in vitro antimicrobial potential of the complexes has been tested by the broth dilution method and the antioxidant method has been done by free radical scavenging analysis. The in vitro methods reveal the outstanding biological characteristics of the copper complexes. The molecular structure of the ligand and its metal (II) complexes has been optimized using Density Functional Theory studies performed by the Gaussian-09 software and their parameters have been discussed. Natural Bond Orbital and Frontier Molecular Orbital analyses have assessed the presence of a metal-ligand bond in complexes. In addition, molecular docking studies have also been performed on antiviral activity of all the complexes using a viral protein and their interacting amino acids.All the metal complexes have the strong tendency to undergo intercalation mode of binding with CT DNA.The optimized geometry and the quantum mechanical examinations are carried out using Gaussian 09W software.The docking of synthesized compounds with SARS-CoV-2 receptor 7ACS protease 7AEH represents the docking of metal complexes.In silico and in vitro analyses of the synthesized compounds.All the metal complexes have the strong tendency to undergo intercalation mode of binding with CT DNA.The optimized geometry and the quantum mechanical examinations are carried out using Gaussian 09W software.The docking of synthesized compounds with SARS-CoV-2 receptor 7ACS protease 7AEH represents the docking of metal complexes.In silico and in vitro analyses of the synthesized compounds. [ABSTRACT FROM AUTHOR]

Flat bands that do not merely arise from weak interactions can produce exotic physical properties, such as superconductivity or correlated many-body effects. The quantum metric can differentiate whether flat bands will result in correlated physics or are merely dangling bonds. A potential avenue for achieving correlated flat bands involves leveraging geometrical constraints within specific lattice structures, such as the kagome lattice; however, materials are often more complex. In these cases, quantum geometry becomes a powerful indicator of the nature of bands with small dispersions. We present a simple, soft-chemical processing route to access a flat band with an extended quantum metric below the Fermi level. By oxidizing Ni-kagome material Cs2Ni3S4 to CsNi3S4, we see a two orders of magnitude drop in the room temperature resistance. However, CsNi3S4 is still insulating, with no evidence of a phase transition. Using experimental data, density functional theory calculations, and symmetry analysis, our results suggest the emergence of a correlated insulating state of unknown origin. [ABSTRACT FROM AUTHOR]

The emergence of strong relativistic spin-orbit effects in low-dimensional systems provides a rich opportunity for exploring unconventional states of matter. Here, we present a route to realise tunable relativistic band structures based on the lateral patterning of proximity-induced spin-orbit coupling. The concept is illustrated on a patterned graphene–transition metal dichalcogenide heterostructure, where the spatially periodic spin-orbit coupling induces a rich mini-band structure featuring massless and massive Dirac bands carrying large spin Berry curvature. The envisaged systems support robust and gate-tunable spin Hall responses driven by the quantum geometry of mini-bands, which can be tailored through metasurface fabrication methods and twisting effects. These findings open pathways to two-dimensional quantum material design and low-power spintronic applications. Engineering sizeable spin-orbit coupling (SOC) in graphene generates effects unmatched in traditional low-dimensional systems. Here, the authors show that the periodic modulation of SOC in 1D patterned graphene heterostructures leads to unusual mini-band structures with symmetry-protected Dirac cones featuring enhanced spin Berry curvature, which paves the way to tunable spin Hall responses. [ABSTRACT FROM AUTHOR]

In this expository paper, we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and Z X -calculus, establishing a connection between quantum computing questions and quantum groups, i.e. Hopf algebras. [ABSTRACT FROM AUTHOR]

It is remarkable that Heisenberg's position-momentum uncertainty relation leads to the existence of a maximal acceleration for a physical particle in the context of a geometric reformulation of quantum mechanics. It is also known that the maximal acceleration of a quantum particle is related to the magnitude of the speed of transportation in projective Hilbert space. In this paper, inspired by the study of geometric aspects of quantum evolution by means of the notions of curvature and torsion, we derive an upper bound for the rate of change of the speed of transportation in an arbitrary finite-dimensional projective Hilbert space. The evolution of the physical system being in a pure quantum state is assumed to be governed by an arbitrary time-varying Hermitian Hamiltonian operator. Our derivation, in analogy to the inequalities obtained by L. D. Landau in the theory of fluctuations by means of general commutation relations of quantum-mechanical origin, relies upon a generalization of Heisenberg's uncertainty relation. We show that the acceleration squared of a quantum evolution in projective space is upper bounded by the variance of the temporal rate of change of the Hamiltonian operator. Moreover, focusing for illustrative purposes on the lower-dimensional case of a single spin qubit immersed in an arbitrarily time-varying magnetic field, we discuss the optimal geometric configuration of the magnetic field that yields maximal acceleration along with vanishing curvature and unit geodesic efficiency in projective Hilbert space. Finally, we comment on the consequences that our upper bound imposes on the limit at which one can perform fast manipulations of quantum systems to mitigate dissipative effects and/or obtain a target state in a shorter time. [ABSTRACT FROM AUTHOR]

In this paper, we review some geometrical aspects pertaining to the world of monotone quantum metrics in finite dimensions. Particular emphasis is given to an unfolded perspective for quantum states that is built out of the spectral theorem and is naturally suited to investigate the comparison with the classical case of probability distributions. [ABSTRACT FROM AUTHOR]

This work introduces a geometrical object that generalizes the quantum geometric tensor; we call it N -bein. Analogous to the vielbein (orthonormal frame) used in the Cartan formalism, the N -bein behaves like a 'square root' of the quantum geometric tensor. Using it, we present a quantum geometric tensor of two states that measures the possibility of moving from one state to another after two consecutive parameter variations. This new tensor determines the commutativity of such variations through its anti-symmetric part. In addition, we define a connection different from the Berry connection, and combining it with the N -bein allows us to introduce a notion of torsion and curvature à la Cartan that satisfies the Bianchi identities. Moreover, the torsion coincides with the anti-symmetric part of the two-state quantum geometric tensor previously mentioned, and thus, it is related to the commutativity of the parameter variations. We also describe our formalism using differential forms and discuss the possible physical interpretations of the new geometrical objects. Furthermore, we define different gauge invariants constructed from the geometrical quantities introduced in this work, resulting in new physical observables. Finally, we present two examples to illustrate these concepts: a harmonic oscillator and a generalized oscillator, both immersed in an electric field. We found that the new tensors quantify correlations between quantum states that were unavailable by other methods. [ABSTRACT FROM AUTHOR]

The control over the geometry and topology of quantum systems is crucial for advancing novel quantum technologies. This work provides a synthesis of recent insights into the behavior of quantum vortices within atomic Bose–Einstein condensates (BECs) subject to curved geometric constraints. We highlight the significant impact of the curvature on the condensate density and phase distribution, particularly in quasi-one-dimensional waveguides for different angular momentum states. An engineered periodic transport of the quantized vorticity between density-coupled ring-shaped condensates is discussed. The significant role of curved geometry in shaping the dynamics of rotational Josephson vortices in long atomic Josephson junctions is illustrated for the system of vertically stacked toroidal condensates. Different methods for the controlled creation of rotational Josephson vortices in coupled ring systems are described in the context of the formation of long-lived vortex configurations in shell-shaped BECs with cylindrical geometry. Future directions of explorations of vortices in curved geometries with implications for quantum information processing and sensing technologies are discussed. [ABSTRACT FROM AUTHOR]

A unified theory is presented for finite-temperature many-body perturbation expansions of the anharmonic vibrational contributions to thermodynamic functions, i.e., the free energy, internal energy, and entropy. The theory is diagrammatically size-consistent at any order, as ensured by the linked-diagram theorem proved in this study, and, thus, applicable to molecular gases and solids on an equal footing. It is also a basis-set-free formalism, just like its underlying Bose–Einstein theory, capable of summing anharmonic effects over an infinite number of states analytically. It is formulated by the Rayleigh–Schrödinger-style recursions, generating sum-over-states formulas for the perturbation series, which unambiguously converges at the finite-temperature vibrational full-configuration-interaction limits. Two strategies are introduced to reduce these sum-over-states formulas into compact sum-over-modes analytical formulas. One is a purely algebraic method that factorizes each many-mode thermal average into a product of one-mode thermal averages, which are then evaluated by the thermal Born–Huang rules. Canonical forms of these rules are proposed, dramatically expediting the reduction process. The other is finite-temperature normal-ordered second quantization, which is fully developed in this study, including a proof of thermal Wick's theorem and the derivation of a normal-ordered vibrational Hamiltonian at finite temperature. The latter naturally defines a finite-temperature extension of size-extensive vibrational self-consistent field theory. These reduced formulas can be represented graphically as Feynman diagrams with resolvent lines, which include anomalous and renormalization diagrams. Two order-by-order and one general-order algorithms of computing these perturbation corrections are implemented and applied up to the eighth order. The results show no signs of Kohn–Luttinger-type nonconvergence. [ABSTRACT FROM AUTHOR]

The application of rare earth (RE) doped crystals in quantum information processing has attracted more and more attention in the past decade. How to change the clock transitions of RE ion in crystal and control their lifetime of maintaining coherent quantum state is a valuable question. In this work, the trigonal 171Yb3+ centers in lithium niobate (LN) crystal are investigated theoretically to obtain their accurate ground and excited hyperfine sublevels under external magnetic field B by a combined method of density functional theory-based geometric optimization and parametric effective Hamiltonian modeling. An optical clock transition at |B| = 45.73 mT along the c axis of the LN crystal is successfully found by calculation. To show the pressure-dependent behavior of optical clock transition, the variation of such transition under hydrostatic pressure up to 3 GPa is also obtained theoretically. The calculated results show that applying external pressure is an effective way to control these transitions of RE ion doped crystal. Moreover, the optical coherence time T2 at zero magnetic field for 171Yb3+ ion with C3 symmetry in the LN crystal is estimated by our calculations. The calculated results indicate that if the magnetic field noise is 33 μT in the LN crystal, it is possible to find an optical clock transition with long coherence time T2 (≈382 μs) at the zero magnetic field. The present methods of seeking optical clock transition and calculating its coherence time T2 caused by a fluctuating magnetic field noise in the host crystal can be applied to other Kramers RE ions doped materials. [ABSTRACT FROM AUTHOR]

Within the nuclear-electronic orbital (NEO) framework, the real-time NEO time-dependent density functional theory (RT-NEO-TDDFT) approach enables the simulation of coupled electronic-nuclear dynamics. In this approach, the electrons and quantum nuclei are propagated in time on the same footing. A relatively small time step is required to propagate the much faster electronic dynamics, thereby prohibiting the simulation of long-time nuclear quantum dynamics. Herein, the electronic Born–Oppenheimer (BO) approximation within the NEO framework is presented. In this approach, the electronic density is quenched to the ground state at each time step, and the real-time nuclear quantum dynamics is propagated on an instantaneous electronic ground state defined by both the classical nuclear geometry and the nonequilibrium quantum nuclear density. Because the electronic dynamics is no longer propagated, this approximation enables the use of an order-of-magnitude larger time step, thus greatly reducing the computational cost. Moreover, invoking the electronic BO approximation also fixes the unphysical asymmetric Rabi splitting observed in previous semiclassical RT-NEO-TDDFT simulations of vibrational polaritons even for small Rabi splitting, instead yielding a stable, symmetric Rabi splitting. For the intramolecular proton transfer in malonaldehyde, both RT-NEO-Ehrenfest dynamics and its BO counterpart can describe proton delocalization during the real-time nuclear quantum dynamics. Thus, the BO RT-NEO approach provides the foundation for a wide range of chemical and biological applications. [ABSTRACT FROM AUTHOR]

Excitons are the neutral quasiparticles that form when Coulomb interactions create bound states between electrons and holes. Due to their bosonic nature, excitons are expected to condense and exhibit superfluidity at sufficiently low temperatures. In interacting Chern insulators, excitons may inherit the nontrivial topology and quantum geometry from the underlying electron wavefunctions. We theoretically investigate the excitonic bound states and superfluidity in flat-band insulators pumped with light. We find that the exciton wavefunctions exhibit vortex structures in momentum space, with the total vorticity being equal to the difference of Chern numbers between the conduction and valence bands. Moreover, both the exciton binding energy and the exciton superfluid density are proportional to the Brillouin-zone average of the quantum metric and the Coulomb potential energy per unit cell. Spontaneous emission of circularly polarized light from radiative decay is a detectable signature of the exciton vorticity. We propose that the vorticity can also be experimentally measured via the nonlinear anomalous Hall effect, whereas the exciton superfluidity can be detected by voltage-drop quantization through a combination of quantum geometry and Aharonov-Casher effect. Topological excitons and their superfluid phase could be realized in flat bands of twisted Van der Waals heterostructures. [ABSTRACT FROM AUTHOR]

Recent years have seen a surge in research on the role of quantum geometry in condensed matter physics. For instance, the Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields due to an obstruction in space associated with a magnetic flux. A similar effect can be observed in solid-state systems, where the topology of the Berry connection can influence electron dynamics. These are paradigmatic examples of how the dynamics can be affected by the system's geometry. Here, we show that in chiral-symmetric processes the quantum metric has a measurable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk and demonstrates an effect that can be attributed directly to the geometry of the state space. Advanced materials are characterized by complex mathematical properties such as the topology and geometry of quantum states. This work demonstrates that in some systems, the evolution of a particle's spatial distribution is a direct measure of these properties: the relative displacement in two sublattices is found to be given by the quantum metric. [ABSTRACT FROM AUTHOR]

Crack detection methods of high-rise building walls based on traditional computer vision (CV) heavily rely on manual selection and extraction of design features. Convolutional neural network (CNN)-based CV can actively learn the features of cracks and adapt to complex backgrounds, solving the limitations of traditional crack detection methods. This paper explores faster region-CNN, single shot multibox detector (SSD), You Only Look Once for crack detection, and Mask R-CNN for crack segmentation and proposes a novel automatic crack geometric quantification method by combining CNN-based object detection and segmentation. The contents include (1) crack detection and bounding box extraction, exploring a variety of models, selecting the best model to detect the image taken by an unmanned aerial vehicle (UAV), and extracting the crack region; (2) crack segmentation, using the detection results of the first part as input for more accurate detection and segmentation of cracks; and (3) a novel pixel-level geometric quantization method of crack based on Hough straight-line detection, mainly including crack length and width. Then, the pixel level is transformed into the actual geometric quantization to simply determine the crack severity. The three models generated in these three parts can be used for managing exterior wall cracks in high-rise buildings for different inspection purposes. [ABSTRACT FROM AUTHOR]

The meaning of the quantum minimum effective length that should distinguish the quantum nature of a gravitational field is investigated in the context of manifestly covariant quantum gravity theory (CQG-theory). In such a framework, the possible occurrence of a non-vanishing minimum length requires one to identify it necessarily with a 4-scalar proper length s.It is shown that the latter must be treated in a statistical way and associated with a lower bound in the error measurement of distance, namely to be identified with a standard deviation. In this reference, the existence of a minimum length is proven based on a canonical form of Heisenberg inequality that is peculiar to CQG-theory in predicting massive quantum gravitons with finite path-length trajectories. As a notable outcome, it is found that, apart from a numerical factor of O 1 , the invariant minimum length is realized by the Planck length, which, therefore, arises as a constitutive element of quantum gravity phenomenology. This theoretical result permits one to establish the intrinsic minimum-length character of CQG-theory, which emerges consistently with manifest covariance as one of its foundational properties and is rooted both on the mathematical structure of canonical Hamiltonian quantization, as well as on the logic underlying the Heisenberg uncertainty principle. [ABSTRACT FROM AUTHOR]

Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The myriad of factors governing shift-current response, however, poses significant challenges in finding such strong shift-current materials. Here we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. We further relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Furthermore, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit an enhanced shift current response. Materials exhibiting a significant shift current response could potentially outperform conventional solar cell materials. The authors propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve an enhanced shift current response. [ABSTRACT FROM AUTHOR]

In this paper, we present a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by state vectors evolving under nonstationary Hamiltonians. Specifically, relying on the existing geometric viewpoint for stationary Hamiltonians, we discuss the generalization of our theoretical construct to time-dependent quantum-mechanical scenarios where both time-varying curvature and torsion coefficients play a key role. Specifically, we present a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced out by a parallel-transported pure quantum state evolving unitarily under a time-dependent Hamiltonian specifying the Schrödinger evolution equation. The time-varying curvature coefficient is specified by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and measures the bending of the quantum curve. The time-varying torsion coefficient, instead, is given by the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 , orthogonal to | T 〉 and | Ψ 〉 and, in addition, measures the twisting of the quantum curve. We find that the time-varying setting exhibits a richer structure from a statistical standpoint. For instance, unlike the time-independent configuration, we find that the notion of generalized variance enters nontrivially in the definition of the torsion of a curve traced out by a quantum state evolving under a nonstationary Hamiltonian. To physically illustrate the significance of our construct, we apply it to an exactly soluble time-dependent two-state Rabi problem specified by a sinusoidal oscillating time-dependent potential. In this context, we show that the analytical expressions for the curvature and torsion coefficients are completely described by only two real three-dimensional vectors, the Bloch vector that specifies the quantum system and the externally applied time-varying magnetic field. Although we show that the torsion is identically zero for an arbitrary time-dependent single-qubit Hamiltonian evolution, we study the temporal behavior of the curvature coefficient in different dynamical scenarios, including off-resonance and on-resonance regimes and, in addition, strong and weak driving configurations. While our formalism applies to pure quantum states in arbitrary dimensions, the analytic derivation of associated curvatures and orbit simulations can become quite involved as the dimension increases. Thus, finally we briefly comment on the possibility of applying our geometric formalism to higher-dimensional qudit systems that evolve unitarily under a general nonstationary Hamiltonian. [ABSTRACT FROM AUTHOR]

The multi-particle Arnol'd cat is a generalization of the Hamiltonian system, both classical and quantum, whose period evolution operator is the renowned map that bears its name. It is obtained following the Joos–Zeh prescription for decoherence by adding a number of scattering particles in the configuration space of the cat. Quantization follows swiftly if the Hamiltonian approach, rather than the semiclassical approach, is adopted. The author has studied this system in a series of previous works, focusing on the problem of quantum–classical correspondence. In this paper, the dynamics of this system are tested by two related yet different indicators: the time autocorrelation function of the canonical position and the out-of-time correlator of position and momentum. [ABSTRACT FROM AUTHOR]

The quantum system behaviour in the presence of a potential is best described by the Schrödinger equation. Maturation of analytical methods in solving the Schrödinger equation for various potentials provides a theorist with powerful tools for better understanding the behaviour of quantum systems. With this objective in mind, this paper introduces a novel potential, called the generalized hyperbolic cotangent potential. This potential is interesting because it encompasses a few exponential-type potentials. A quantum system interacting with such a potential, therefore, warrants careful study. The paper presents analytical solutions to the bound state problem of the generalized hyperbolic cotangent potential for arbitrary l states using a newly established quantization rule. Towards this end, the analytical formula is derived for the energy eigenvalue and respective eigenstate. Special cases of the analytical formula of the energy spectrum are discussed for the generalized hyperbolic cotangent potential. [ABSTRACT FROM AUTHOR]

Non-centrosymmetric topological material has attracted intense attention due to its superior characteristics as compared with the centrosymmetric one, although probing the local quantum geometry in non-centrosymmetric topological material remains challenging. The non-linear Hall (NLH) effect provides an ideal tool to investigate the local quantum geometry. Here, we report a non-centrosymmetric topological phase in ZrTe5, probed by using the NLH effect. The angle-resolved and temperature-dependent NLH measurement reveals the inversion and ab-plane mirror symmetries breaking at <30 K, consistently with our theoretical calculation. Our findings identify a new non-centrosymmetric phase of ZrTe5 and provide a platform to probe and control local quantum geometry via crystal symmetries. [ABSTRACT FROM AUTHOR]

A continuous bundle of C ∗ -algebras provides a rigorous framework to study the thermodynamic limit of quantum theories. If the bundle admits the additional structure of a strict deformation quantization (in the sense of Rieffel) one is allowed to study the classical limit of the quantum system, i.e. a mathematical formalism that examines the convergence of algebraic quantum states to probability measures on phase space (typically a Poisson or symplectic manifold). In this manner, we first prove the existence of the classical limit of Gibbs states illustrated with a class of Schrödinger operators in the regime where Planck's constant ℏ appearing in front of the Laplacian approaches zero. We additionally show that the ensuing limit corresponds to the unique probability measure satisfying the so-called classical or static KMS-condition. Subsequently, we conduct a similar study on the free energy of mean-field quantum spin systems in the regime of large particles, and discuss the existence of the classical limit of the relevant Gibbs states. Finally, a short section is devoted to single site quantum spin systems in the large spin limit. [ABSTRACT FROM AUTHOR]

We study the Poisson geometrical formulation of quantum mechanics for finite dimensional mixed and pure states. Equivalently, we show that quantum mechanics can be understood in the language of classical mechanics. We review the symplectic structure of the Hilbert space and identify its canonical coordinates. We extend the geometric picture to the space of density matrices D N + . We find it is not symplectic but admits a linear s u (N) Poisson structure. We identify Casimir surfaces of D N + and show that the space of pure states P N ≡ C P N − 1 is one of its symplectic submanifolds which is an intersection of primitive Casimirs. We identify generic symplectic submanifolds of D N + and calculate their dimensions. We find that D N + is singularly foliated by the symplectic leaves of varying dimensions, also known as coadjoint orbits. We also find an ascending chain of Poisson submanifolds D N M ⊂ D N M + 1 for 1 ≤ M ≤ N − 1. Each such Poisson submanifold D N M is obtained by tracing out the C M states from the bipartite system C N × C M and is an intersection of N − M primitive Casimirs of D N + . Their Poisson structure is induced from the symplectic structure of the bipartite system. We also show their foliations. Finally, we study the positive semi-definite geometry of the symplectic submanifold E N M consisting of the mixed states with maximum entropy in D N M . [ABSTRACT FROM AUTHOR]

In this paper, we construct a bi-covariant (h,h′)-deformed differential calculus on the Hopf superalgebra of functions on the quantum supergroup GL h.h ′ (1|1) and obtain an extended differential calculus (Cartan calculus) by including inner derivations and Lie derivatives. In doing so, we use left-Cartan-Maurer 1-forms and left-vector fields. [ABSTRACT FROM AUTHOR]

Given a simple, simply connected, complex algebraic group G, a flat projective connection on the bundle of non-abelian theta functions on the moduli space of semistable parabolic G-bundles over any family of smooth projective curves with marked points was constructed by the authors in an earlier paper. Here, it is shown that the identification between the bundle of non-abelian theta functions and the bundle of WZW conformal blocks is flat with respect to this connection and the one constructed by Tsuchiya–Ueno–Yamada. As an application, we give a geometric construction of the Knizhnik–Zamolodchikov connection on the trivial bundle over the configuration space of points in the projective line whose typical fiber is the space of invariants of tensor product of representations. [ABSTRACT FROM AUTHOR]

We report a first-principles investigation based on density functional theory with the Hubbard U correction to identify the mechanism behind the electric-field modulation, via a - c domain-wall motion, of the anisotropic magnetoresistance (AMR) ratio in C o 2 FeSi / BaTi O 3 heterostructures. The effects of BaTi O 3 (BTO) electric polarization in the [ 001 ], [ 00 1 ¯ ], and [ 0 1 ¯ 0 ] directions on the FeSi / Ti O 2 and CoCo / Ti O 2 interface terminations are taken into account. We show that the response of the interface geometric and electronic properties to the BTO polarization depends on the interface termination. For instance, the pinning of atoms at the FeSi -terminated interface inhibits the [ 001 ] polarization. Through the a - c domain-wall motion, interface hybridized 3 d y z states shift in energy and change the minority-spin density of states at the Fermi level, modifying the AMR through the α = ρ ↓ ρ ↑ component. A discussion of the results based on the Campbell–Fert–Jaoul model with s - s and s - d scattering is provided. The electronic states of C o 2 FeSi inner layers remained mostly unchanged upon the transition between the ferroelectric domains, which indicates that long-range magnetoelastic effects have a negligible influence on the AMR ratio. Hence, the results indicate that interface bonding effects are the origin of the electric-field modulation of the AMR via a - c domain-wall motion in C o 2 FeSi / BaTi O 3 heterostructures. [ABSTRACT FROM AUTHOR]

This work develops and illustrates a new method of calculating "chemically accurate" electronic wavefunctions (and energies) via a truncated full configuration interaction (CI) procedure, which arguably circumvents the large matrix diagonalization that is the core problem of full CI and is also central to modern selective CI approaches. This is accomplished simply by following the standard/ubiquitous Davidson method in its "direct" form—wherein, in each iteration, the electronic Hamiltonian operator is applied directly in second quantization to the Ritz vector/wavefunction from the prior iteration—except that (in this work) only a small portion of the resultant expansion vector is actually even computed (through the application of only a similarly small portion of the Hamiltonian). Specifically, at each iteration of this truncated Davidson approach, the new expansion vector is taken to be twice as large as that from the prior iteration. In this manner, a small set of highly truncated expansion vectors (say 10–30) of increasing precision is incrementally constructed, forming a small subspace within which diagonalization of the Hamiltonian yields clear, consistent, and monotonically variational convergence to the approximate full CI limit. The good efficiency in which convergence to the level of chemical accuracy (1.6 mhartree) is achieved suggests, at least for the demonstrated problem sizes—Hilbert spaces of 1018 and wavefunctions of 108 determinants—that this truncated Davidson methodology can serve as a replacement of standard CI and complete-active space approaches in circumstances where only a few chemically significant digits of accuracy are required and/or meaningful in view of ever-present basis set limitations. [ABSTRACT FROM AUTHOR]

We present an algorithmic framework for quantum-inspired classical algorithms on close-to-low-rank matrices, generalizing the series of results started by Tang's breakthrough quantum-inspired algorithm for recommendation systems [STOC'19]. Motivated by quantum linear algebra algorithms and the quantum singular value transformation (SVT) framework of Gilyén et al. [STOC'19], we develop classical algorithms for SVT that run in time independent of input dimension, under suitable quantum-inspired sampling assumptions. Our results give compelling evidence that in the corresponding QRAM data structure input model, quantum SVT does not yield exponential quantum speedups. Since the quantum SVT framework generalizes essentially all known techniques for quantum linear algebra, our results, combined with sampling lemmas from previous work, suffice to generalize all prior results about dequantizing quantum machine learning algorithms. In particular, our classical SVT framework recovers and often improves the dequantization results on recommendation systems, principal component analysis, supervised clustering, support vector machines, low-rank regression, and semidefinite program solving. We also give additional dequantization results on low-rank Hamiltonian simulation and discriminant analysis. Our improvements come from identifying the key feature of the quantum-inspired input model that is at the core of all prior quantum-inspired results: -2-norm sampling can approximate matrix products in time independent of their dimension. We reduce all our main results to this fact, making our exposition concise, self-contained, and intuitive. [ABSTRACT FROM AUTHOR]

It has been recently shown in Chatterjee and Ghosh (Phys Rev Lett 125:041302, 2020, https://doi.org/10.1103/PhysRevLett.125.041302) that microstate counting carried out for quantum states residing on the horizon of a black hole leads to a correction of the form exp (- A / 4 l p 2) in the Bekenstein-Hawking form of the black hole entropy. In this paper, we develop a novel approach to obtain the possible form of the spacetime geometry from the entropy of the black hole for a given horizon radius. The uniqueness of this solution for a given energy-momentum tensor has also been discussed. Remarkably, the black hole geometry reconstructed has striking similarities to that of noncommutative-inspired Schwarzschild black holes (Nicolini et al. in Phys Lett B 632:547, 2006). We also obtain the matter density functions using Einstein field equations for the geometries we reconstruct from the thermodynamics of black holes. These also have similarities to that of the matter density function of a noncommutative-inspired Schwarzschild black hole. The conformal structure of the metric is briefly discussed and the Penrose–Carter diagram is drawn. We then compute the Komar energy and the Smarr formula for the effective black hole geometry and compare it with that of the noncommutative-inspired Schwarzschild black hole. We also discuss some astrophysical implications of the solutions. Finally, we propose a set of quantum Einstein vacuum field equations, as a solution of which we obtain one of the spacetime solutions obtained in this work. We then show a direct connection between the quantum Einstein vacuum field equations and the first law of black hole thermodynamics. [ABSTRACT FROM AUTHOR]

Quantum physics is intrinsically probabilistic, where the Born rule yields the probabilities associated with a state that deterministically evolves. The entropy of a quantum state quantifies the amount of randomness (or information loss) of such a state. The degrees of freedom of a quantum state are position and spin. We focus on the spin degree of freedom and elucidate the spin-entropy. Then, we present some of its properties and show how entanglement increases spin-entropy. A dynamic model for the time evolution of spin-entropy concludes the paper. [ABSTRACT FROM AUTHOR]

This study explores the age-old quest to construct a geometric model of a quantum particle. While static classical particle models have largely been dismissed, the focus has now shifted to intricate dynamic models that hold the promise of reconciling general relativity with quantum mechanics. We propose that matter particles can be described as radiation confined within dynamically curved spacetime regions, without the need for quantization of space and time, and using standard field equations and natural Planck units. Specifically, we investigate a cyclic or oscillating radiation-dominated micro-cosmos undergoing repeated bouncing. Our methodology employs integration, with carefully defined initial conditions. The results include several observable properties characteristic of quantum particles. We calculate the total mass, revealing a compelling inverse proportionality between mass and radius identical with the de Broglie relationship. Applying this model to protons, we discover a profound and surprisingly simple relationship between the proton's radius and mass expressed in Planck units. This enables a definition of the proton radius that aligns remarkably well with the 2018 CODATA value. Furthermore, our analysis demonstrates that the radial density profile of the proton (or nucleon), averaged over a cycle time, increases toward the center. The problem of embedding the micro-cosmos within a background spacetime is also described. These results underscore the relevance of general relativity in the domain of nuclear physics. Moreover, the model offers a fresh perspective that can stimulate new ideas in the ongoing quest to unify general relativity with quantum physics. [ABSTRACT FROM AUTHOR]

Cosmic censorship protects the outside world from black hole singularities and paves the way for assigning entropy to gravity at the event horizons. We point out a tension between cosmic censorship and the quantum backreacted geometry of Schwarzschild black holes, induced by vacuum polarization and driven by the conformal anomaly. A similar tension appears for the Weyl curvature hypothesis at the Big Bang singularity. We argue that the requirement of exact conformal symmetry resolves both conflicts and has major implications for constraining the set of fundamental constituents of the Standard Model. [ABSTRACT FROM AUTHOR]

We give a path integral construction of the quantum mechanical partition function for gauged finite groups. Our construction gives the quantization of a system of d, N × N matrices invariant under the adjoint action of the symmetric group SN. The approach is general to any discrete group. For a system of harmonic oscillators, i.e. for the non-interacting case, the partition function is given by the Molien-Weyl formula times the zero-point energy contribution. We further generalise the result to a system of non-square and complex matrices transforming under arbitrary representations of the gauge group. [ABSTRACT FROM AUTHOR]

This article focuses on three main contributions. Firstly, we provide an in-depth overview of the nonlocal Lagrangian formalism. Secondly, we introduce an extended version of the second Noether's theorem tailored for nonlocal Lagrangians. Finally, we apply both the formalism and the extended theorem to the context of non-commutative U(1) gauge theory, including its Hamiltonian and quantization, showcasing their practical utility. [ABSTRACT FROM AUTHOR]

In this paper we would like to highlight the problems of conceiving the "Hydrogen Bond" (HB) as a real short-range, directional, electrostatic, attractive interaction and to reframe its nature through the non-approximated view of condensed matter offered by a Quantum Electro-Dynamic (QED) perspective. We focus our attention on water, as the paramount case to show the effectiveness of this 40-year-old theoretical background, which represents water as a two-fluid system (where one of the two phases is coherent). The HB turns out to be the result of the electromagnetic field gradient in the coherent phase of water, whose vacuum level is lower than in the non-coherent (gas-like) fraction. In this way, the HB can be properly considered, i.e., no longer as a "dipolar force" between molecules, but as the phenomenological effect of their collective thermodynamic tendency to occupy a lower ground state, compatible with temperature and pressure. This perspective allows to explain many "anomalous" behaviours of water and to understand why the calculated energy associated with the HB should change when considering two molecules (water-dimer), or the liquid state, or the different types of ice. The appearance of a condensed, liquid, phase at room temperature is indeed the consequence of the boson condensation as described in the context of spontaneous symmetry breaking (SSB). For a more realistic and authentic description of water, condensed matter and living systems, the transition from a still semi-classical Quantum Mechanical (QM) view in the first quantization to a Quantum Field Theory (QFT) view embedded in the second quantization is advocated. [ABSTRACT FROM AUTHOR]

We construct a Wick-type deformation quantization of contact metric manifolds. The construction is fully canonical and involves no arbitrary choice. Unlike the case of symplectic or Poisson manifolds, not every classical observable on a general contact metric manifold can be promoted to a quantum one due to possible obstructions to quantization. We prove, however, that all these obstructions disappear for Sasakian manifolds. [ABSTRACT FROM AUTHOR]

Due to the classifying theorems by Petz and Kubo–Ando, we know that there are bijective correspondences between Quantum Fisher Information(s), operator means, and the class of symmetric, normalized operator monotone functions on the positive half line; this last class is usually denoted as  F o p . This class of operator monotone function has a significant structure, which is worthy of study; indeed, any step in understanding  F o p , besides being interesting per se, immediately translates into a property of the classes of operator means and therefore of Quantum Fisher Information(s). In recent years, the  f ↔ f  correspondence has been introduced, which associates a non-regular element of  F o p  to any regular element of the same set. In terms of operator means, this amounts to associating a mean with multiplicative character to a mean that has an additive character. In this paper, we survey a number of different settings where this technique has proven useful in Quantum Information Geometry. In Sections 1–4, all the needed background is provided. In Sections 5–14, we describe the main applications of the  f ↔ f ˜  correspondence. [ABSTRACT FROM AUTHOR]

We present algorithms and a C code to reveal quantum contextuality and evaluate the contextuality degree (a way to quantify contextuality) for a variety of point-line geometries located in binary symplectic polar spaces of small rank. With this code we were not only able to recover, in a more efficient way, all the results of a recent paper by de Boutray et al. [(2022). Journal of Physics A: Mathematical and Theoretical 55 475301], but also arrived at a bunch of new noteworthy results. The paper first describes the algorithms and the C code. Then it illustrates its power on a number of subspaces of symplectic polar spaces whose rank ranges from 2 to 7. The most interesting new results include: (i) non-contextuality of configurations whose contexts are subspaces of dimension 2 and higher, (ii) non-existence of negative subspaces of dimension 3 and higher, (iii) considerably improved bounds for the contextuality degree of both elliptic and hyperbolic quadrics for rank 4, as well as for a particular subgeometry of the three-qubit space whose contexts are the lines of this space, (iv) proof for the non-contextuality of perpsets and, last but not least, (v) contextual nature of a distinguished subgeometry of a multi-qubit doily, called a two-spread, and computation of its contextuality degree. Finally, in the three-qubit polar space we correct and improve the contextuality degree of the full configuration and also describe finite geometric configurations formed by unsatisfiable/invalid constraints for both types of quadrics as well as for the geometry whose contexts are all 315 lines of the space. [ABSTRACT FROM AUTHOR]

The DC photocurrent can detect the topology and geometry of quantum materials without inversion symmetry. Herein, we propose that the DC shot noise (DSN), as the fluctuation of photocurrent operator, can also be a diagnostic of quantum materials. Particularly, we develop the quantum theory for DSNs in gapped systems and identify the shift and injection DSNs by dividing the second-order photocurrent operator into off-diagonal and diagonal contributions, respectively. Remarkably, we find that the DSNs can not be forbidden by inversion symmetry, while the constraint from time-reversal symmetry depends on the polarization of light. Furthermore, we show that the DSNs also encode the geometrical information of Bloch electrons, such as the Berry curvature and the quantum metric. Finally, guided by symmetry, we apply our theory to evaluate the DSNs in monolayer GeS and bilayer MoS2 with and without inversion symmetry and find that the DSNs can be larger in centrosymmetric phase. The bulk photovoltaic effect and DC photocurrent generation can be used to detect topology and geometry in non-centrosymmetric quantum materials. Here, the authors theoretically propose the detection of DC shot noise as a diagnostic tool for the characterization of the band quantum geometry under relaxed symmetry conditions. [ABSTRACT FROM AUTHOR]

We generalize Koopman–von Neumann classical mechanics to poly symplectic fields and recover De Donder–Weyl's theory. Compared with Dirac's Hamiltonian density, it inspires a new Hamiltonian formulation with a canonical momentum field that is Lorentz-covariant with symplectic geometry. We provide commutation relations for the classical and quantum fields that generalize the Koopman–von Neumann and Heisenberg algebras. The classical algebra requires four fields that generalize spacetime, energy–momentum, frequency–wavenumber, and the Fourier conjugate of energy–momentum. We clarify how first and second quantization can be found by simply mapping between operators in classical and quantum commutator algebras. [ABSTRACT FROM AUTHOR]

We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian. [ABSTRACT FROM AUTHOR]

A longstanding enigma within AdS/CFT concerns the entanglement entropy of holographic quantum fields in Rindler space. The vacuum of a quantum field in Minkowski spacetime can be viewed as an entangled thermofield double of two Rindler wedges at a temperature T = 1/2π. We can gradually disentangle the state by lowering this temperature, and the entanglement entropy should vanish in the limit T → 0 to the Boulware vacuum. However, holography yields a non-zero entanglement entropy at arbitrarily low T, since the bridge in the bulk between the two wedges retains a finite width. We show how this is resolved by bulk quantum effects of the same kind that affect the entropy of near-extremal black holes. Specifically, a Weyl transformation maps the holographic Boulware states to near-extremal hyperbolic black holes. A reduction to an effective two-dimensional theory captures the large quantum fluctuations in the geometry of the bridge, which bring down to zero the density of entangled states in the Boulware vacuum. Using another Weyl transformation, we construct unentangled Boulware states in de Sitter space. [ABSTRACT FROM AUTHOR]

In a previous paper, the author and his collaborator studied the problem of lifting Hamiltonian group actions on symplectic varieties and Lagrangian subvarieties to their graded deformation quantizations and apply the general results to coadjoint orbit method for semisimple Lie groups. Only even quantizations were considered there. In this paper, these results are generalized to the case of general quantizations with arbitrary periods. The key step is to introduce an enhanced version of the (truncated) period map defined by Bezrukavnikov and Kaledin for quantizations of any smooth symplectic variety X, with values in the space of Picard Lie algebroid over X. As an application, we study quantizations of nilpotent orbits of real semisimple groups satisfying certain codimension condition. [ABSTRACT FROM AUTHOR]

Epitaxially grown quantum dot (QD) lasers in narrow pockets on patterned silicon photonics wafers present a key step toward full monolithic integration of on‐chip light sources. However, InAs QD lasers grown in deep and narrow pockets demonstrate limited performance and reliability compared to planar‐grown counterparts. Herein, InAs QD lasers are grown in patterned SiO2 pockets atop planar thermal cyclic annealed GaAs on (001) Si substrate with reduced threading dislocation density, enabling detailed study of how pocket geometry impacts device performance. Fabry–Pérot lasers with cleaved facets exhibit strong variation in performance based on the dimensions of the pocket, wherein thermal and optical metrics improve with increasing pocket width. Devices lase up to a maximum stage temperature of 115 °C with an extrapolated lifetime of 2.2 years at 80 °C for material grown in 50 μm by 3900 μm pockets. This study addresses, the ongoing challenge of optimizing pocket‐grown devices to planar equivalent performance. [ABSTRACT FROM AUTHOR]

In this article, we highlight that the interaction potential confining Dirac particles in a box must be invariant under the charge conjugation to avoid the Klein paradox, in which an infinite number of negative-energy particles are excited. Furthermore, we derive the quantization rules for a relativistic particle in a cylindrical box, which emulates the volume occupied by a beam of particles with a non-trivial aspect ratio. We apply our results to the evaluation of the quantum limit for emittance in particle accelerators. The developed theory allows the description of quantum beams carrying Orbital Angular Momentum (OAM). We demonstrate how the degeneracy pressure is such to increase the phase–space area of Dirac particles carrying OAM. The results dramatically differ from the classical evaluation of phase–space areas, that would foresee no increase in emittance for beams in a coherent state of OAM. We discuss the quantization of the phase–space cell's area for single Dirac particles carrying OAM, and, finally, provide an interpretation of the beam entropy as the measure of how much the phase–space area occupied by the beam deviates from its quantum limit. [ABSTRACT FROM AUTHOR]

When studying the geometry of quantum states, it is acknowledged that mixed states can be distinguished by infinitely many metrics. Unfortunately, this freedom causes metric-dependent interpretations of physically significant geometric quantities such as the complexity and volume of quantum states. In this paper, we present an insightful discussion on the differences between the Bures and the Sjöqvist metrics inside a Bloch sphere. First, we begin with a formal comparative analysis between the two metrics by critically discussing three alternative interpretations for each metric. Second, we explicitly illustrate the distinct behaviors of the geodesic paths on each one of the two metric manifolds. Third, we compare the finite distances between an initial state and the final mixed state when calculated with the two metrics. Interestingly, in analogy with what happens when studying the topological aspects of real Euclidean spaces equipped with distinct metric functions (for instance, the usual Euclidean metric and the taxicab metric), we observe that the relative ranking based on the concept of a finite distance between mixed quantum states is not preserved when comparing distances determined with the Bures and the Sjöqvist metrics. Finally, we conclude with a brief discussion on the consequences of this violation of a metric-based relative ranking on the concept of the complexity and volume of mixed quantum states. [ABSTRACT FROM AUTHOR]