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Quantum dynamics simulations are becoming a powerful tool for understanding photo-excited molecules. Their poor scaling, however, means that it is hard to study molecules with more than a few atoms accurately, and a major challenge at the moment is the inclusion of the molecular environment. Here, we present a proof of principle for a way to break the two bottlenecks preventing large but accurate simulations. First, the problem of providing the potential energy surfaces for a general system is addressed by parameterizing a standard force field to reproduce the potential surfaces of the molecule's excited-states, including the all-important vibronic coupling. While not shown here, this would trivially enable the use of an explicit solvent. Second, to help the scaling of the nuclear dynamics propagation, a hierarchy of approximations is introduced to the variational multi-configurational Gaussian method that retains the variational quantum wavepacket description of the key quantum degrees of freedom and uses classical trajectories for the remaining in a quantum mechanics/molecular mechanics like approach. The method is referred to as force field quantum dynamics (FF-QD), and a two-state ππ*/nπ* model of uracil, excited to its lowest bright ππ* state, is used as a test case. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the time evolution of quantum coherence—the off-diagonal elements of the density matrix of a multistate quantum system—from the perspective of the Wigner–Moyal formalism. This approach provides an exact phase space representation of quantum mechanics. We consider the coherent evolution of nuclear wavepackets in a molecule with two electronic states. For harmonic potentials, the problem is analytically soluble for both a fully quantum mechanical description and a semiclassical description. We highlight the serious deficiencies of the semiclassical treatment of coherence for general systems and illustrate how even qualitative accuracy requires higher order terms in the Moyal expansion to be included. The model provides an experimentally relevant example of a molecular Schrödinger's cat state. The alive and dead cats of the exact two-state quantum evolution collapse into a "zombie" cat in the semiclassical limit—an averaged behavior, neither alive nor dead, leading to significant errors. The inclusion of the Moyal correction restores a faithful simultaneously alive and dead representation of the cat that is experimentally observable. [ABSTRACT FROM AUTHOR]

We review some recent results on the mathematical foundations of a quantum theory over a scalar field that is a quadratic extension of the non-Archimedean field of p -adic numbers. In our approach, we are inspired by the idea — first postulated in [I. V. Volovich, p -adic string, Class. Quantum Grav. 4 (1987) L83–L87] — that space, below a suitably small scale, does not behave as a continuum and, accordingly, should be modeled as a totally disconnected metrizable topological space, ruled by a metric satisfying the strong triangle inequality. The first step of our construction is a suitable definition of a p -adic Hilbert space. Next, after introducing all necessary mathematical tools — in particular, various classes of linear operators in a p -adic Hilbert space — we consider an algebraic definition of physical states in p -adic quantum mechanics. The corresponding observables, whose definition completes the statistical interpretation of the theory, are introduced as SOVMs, a p -adic counterpart of the POVMs associated with a standard quantum system over the complex numbers. Interestingly, it turns out that the typical convex geometry of the space of states of a standard quantum system is replaced, in the p -adic setting, with an affine geometry; therefore, a symmetry transformation of a p -adic quantum system may be defined as a map preserving this affine geometry. We argue that, as a consequence, the group of all symmetry transformations of a p -adic quantum system has a richer structure with respect to the case of standard quantum mechanics over the complex numbers. [ABSTRACT FROM AUTHOR]

Geometrical methods in quantum information are very promising for both providing technical tools and intuition into difficult control or optimization problems. Moreover, they are of fundamental importance in connecting pure geometrical theories, like GR, to quantum mechanics, like in the AdS/CFT correspondence. In this paper, we first make a survey of the most important settings in which geometrical methods have proven useful to quantum information theory. Then we lay down a geometric theory of entanglement by a principle of action, discussing a simple example with two qubits and consequences for a quantum theory of space-time. [ABSTRACT FROM AUTHOR]

I address the recent debate between Alexander Meehan and Lev Vaidman concerning the claim made by the former for a new problem to quantum mechanics. I argue that while Meehan's incompatibility claim does hold in the situation he presents, it does not genuinely involve considerations that can limit quantum state preparation, nor does it introduce new constrains over possible interpretations of quantum theory. [ABSTRACT FROM AUTHOR]

Molecular imprinting is a promising approach for developing polymeric materials as artificial receptors. However, only a few types of molecularly imprinted polymers (MIPs) are commercially available, and most research on MIPS is still in the experimental phase. The significant limitation has been a challenge for screening imprinting systems, particularly for weak functional target molecules. Herein, a combined method of quantum mechanics (QM) computations and molecular dynamics (MD) simulations was employed to screen an appropriate 2,4-dichlorophenoxyacetic acid (2,4-D) imprinting system. QM calculations were performed using the Gaussian 09 software. MD simulations were conducted using the Gromacs2018.8 software suite. The QM computation results were consistent with those of the MD simulations. In the MD simulations, a realistic model of the 'actual' pre-polymerisation mixture was obtained by introducing numerous components in the simulations to thoroughly investigate all non-covalent interactions during imprinting. This study systematically examined MIP systems using computer simulations and established a theoretical prediction model for the affinity and selectivity of MIPs. The combined method of QM computations and MD simulations provides a robust foundation for the rational design of MIPs. [ABSTRACT FROM AUTHOR]

The problem of the two-dimensional motion of a charged particle with constant mass in the presence of a uniform constant perpendicular magnetic field features in several undergraduate and graduate quantum physics textbooks. This problem is very important to studies of two-dimensional materials that manifest quantum Hall behavior, as evidenced by several major discoveries over the last few years. Many real experimental samples are more complicated due to the anisotropic mass of the electrons. In this work, we provide the exact solution to this problem by means of a clever scaling of coordinates. Calculations are done for a symmetric gauge of the magnetic field. This study allows a broad audience of students and teachers to understand the mathematical techniques that lead to the solution of this quantum problem. Editor's note: The behavior of an electron confined to move in two dimensions in the presence of a perpendicular magnetic field underlies the quantum Hall effect. This is also an analytically solvable problem, so it is valuable to quantum mechanics pedagogy. This paper reviews the solution and then shows a neat trick for solving the problem when the electron's effective mass is anisotropic, a situation that is fairly common in solid-state systems. [ABSTRACT FROM AUTHOR]

In this article I will focus on the debate on the causality principle that originated in the light of quantum mechanics concerning Moritz Schlick and Karl Popper. The discovery of quantum mechanics led to a broad debate on the interpretation of the principle of causality. Schlick proposed that it should be understood as an empirically verifiable postulate, and therefore with limits regarding causal indeterminacy in quantum physics. This approach had an influence on some scientists, especially Werner Heisenberg. However, Popper would develop a different way of understanding science because of the role played by unverifiable elements in theories that can nevertheless be falsified. It is precisely the discussion around the principle of causality that opens up different ways of understanding science. I will first try to analyse Schlick’s argument in the context of the debate that was taking place in the late 1920s in the light of the new quantum mechanics; secondly, I will look at the reception that Schlick’s idea of causality had in Heisenberg and the Copenhagen Interpretation; thirdly, I will analyse Popper’s argument against Schlick’s interpretation; finally, I will try to see the resonances of this debate in Heisenberg and other physicists. [ABSTRACT FROM AUTHOR]

Classical and quantum mechanical descriptions of motion are fundamentally different. The Universality of Free Fall (UFF) is a distinguishing feature of the classical motion (which has been verified with astonishing precision), while quantum theory tell us only about probabilities and uncertainties thus breaking the UFF. There are strong reasons to believe that the classical description must emerge, under plausible hypothesis, from quantum mechanics. In this paper, we show that the UFF is an emergent phenomenon: the coarse-grained quantum distribution for high-energy levels leads to the classical distribution as the lowest order plus quantum corrections. We estimate the size of these corrections on the Eötvös parameter and discuss the physical implications. [ABSTRACT FROM AUTHOR]

The virial theorem is established in the framework of resolution-scale relativity for stochastic dynamics characterized by a diffusion constant . It only relies on a simple time average just like the classical virial theorem, while the quantum mechanical virial theorem involves the expectation values of the observables. Nevertheless, by the emergence of a quantum-like potential term, the resolution-scale relativity virial theorem also encompasses quantum mechanical dynamics under the identification ℏ ↔ 2 m . This provides an illustration of the resolution-scale relativistic approach to the foundation of standard quantum mechanics. Furthermore, it is pointed out that if the resolution-scale relativity principle is implemented in macroscopic systems that are complex and/or chaotic, then the application of the classical virial theorem in the analysis of the dynamics of astrophysical systems neglects the contribution from a resolution-scale relativistic quantum-like potential. It is shown that this quantum-like potential could account for some fraction of the dark matter hypothesis. [ABSTRACT FROM AUTHOR]

This work is a generalization of (Raimundo et al 2021 Phys. Rev. A 103 022201) to Grassmann algebras of arbitrary dimensions. Here we present a covariant quantization scheme for pseudoclassical theories focused on non-hermitian quantum mechanics. The quantization maps canonically related pseudoclassical theories to equivalent quantum realizations in arbitrary dimensions. We apply the formalism to the problem of two coupled spins with Heisenberg interaction. [ABSTRACT FROM AUTHOR]

It is known that the Frenet–Serret apparatus of a space curve in three-dimensional Euclidean space determines the local geometry of curves. In particular, the Frenet–Serret apparatus specifies important geometric invariants, including the curvature and the torsion of a curve. It is also acknowledged in quantum information science that low complexity and high efficiency are essential features to achieve when cleverly manipulating quantum states that encode quantum information about a physical system. In this paper, we propose a geometric perspective on how to quantify the bending and the twisting of quantum curves traced by dynamically evolving state vectors. Specifically, we propose a quantum version of the Frenet–Serret apparatus for a quantum trajectory in projective Hilbert space traced by a parallel-transported pure quantum state evolving unitarily under a stationary Hamiltonian specifying the Schrödinger equation. Our proposed constant curvature coefficient is given by the magnitude squared of the covariant derivative of the tangent vector | T 〉 to the state vector | Ψ 〉 and represents a useful measure of the bending of the quantum curve. Our proposed constant torsion coefficient, instead, is defined in terms of the magnitude squared of the projection of the covariant derivative of the tangent vector | T 〉 , orthogonal to both | T 〉 and | Ψ 〉. The torsion coefficient provides a convenient measure of the twisting of the quantum curve. Remarkably, we show that our proposed curvature and torsion coefficients coincide with those existing in the literature, although introduced in a completely different manner. Interestingly, not only we establish that zero curvature corresponds to unit geodesic efficiency during the quantum transportation in projective Hilbert space, but we also find that the concepts of curvature and torsion help enlighten the statistical structure of quantum theory. Indeed, while the former concept can be essentially defined in terms of the concept of kurtosis, the positivity of the latter can be regarded as a restatement of the well-known Pearson inequality that involves both the concepts of kurtosis and skewness in mathematical statistics. Finally, not only do we present illustrative examples with nonzero curvature for single-qubit time-independent Hamiltonian evolutions for which it is impossible to generate torsion, but we also discuss physical applications extended to two-qubit stationary Hamiltonians that generate curves with both nonzero curvature and nonvanishing torsion traced by quantum states with different degrees of entanglement, ranging from separable states to maximally entangled Bell states. In the Appendix C, we examine the different curvature and torsion characteristics of the three qubit | GHZ 〉 and | W 〉 states under evolution by a quantum Heisenberg Hamiltonian. [ABSTRACT FROM AUTHOR]

This article forms part of a series on "openness," "non-linearity," and "embodiedhealth" in the post-physical, informational (virtual) era of society. This is vital given that the threats posed by advances in artificial intelligence call for a holistic, embodied approach. Typically, health is separated into different categories, for example, (psycho)mental health, biological/bodily health, genetic health, environmental health, or reproductive health. However, this separation only serves to undermine health; there can be no separation of health into subgroups (psychosomatics, for example). Embodied health contains no false divisions and relies on "optimism" as the key framing value. Optimism is only achieved through the mechanism/enabling condition of openness. Openness is vital to secure the embodied health for individuals and societies. Optimism demands that persons become active participants within their own lives and are not mere blank slates, painted in the colors of physical determinism (thus a move away from nihilism-which is the annihilation of freedom/autonomy/ quality). To build an account of embodied health, the following themes/aims are analyzed, built, and validated: (1) a modern re-interpretation and validation of German idealism (the crux of many legal-ethical systems) and Freud; (2) ascertaining the bounded rationality and conceptual semantics of openness (which underlies thermodynamics, psychosocial relations, individual autonomy, ethics, and as being a central constitutional governmental value for many regulatory systems); (3) the link between openness and societal/individual embodied health, freedom, and autonomy; (4) securing the role of individualism/ subjectivity in constituting openness; (5) the vital role of nonlinear dynamics in securing optimism and embodied health; (6) validation of arguments using the methodological scientific value of invariance (generalization value) by drawing evidence from (i) information and computer sciences, (ii) quantum theory, and (iii) bio-genetic evolutionary evidence; and (7) a validation and promotion of the inalienable role of theoretic philosophy in constituting embodied health, and how modern society denigrates embodied health, by misconstruing and undermining theoretics. Thus, this paper provides and defends an up-to-date non-physical account of embodied health by creating a psychophysical-biological-computational-philosophical construction. Thus, this paper also brings invaluable coherence to legal and ethical debates on points of technicality from the empirical sciences, demonstrating that each field is saying the same thing. [ABSTRACT FROM AUTHOR]

Designing a relevant and engaging curriculum for biochemistry undergraduates can be challenging for topics which are at the periphery of the subject. We have used the framework of context‐based learning as a means of assessing understanding of quantum theory in a group of students in their junior year. Our context, the role of retinol in skincare, provides a basis for the simple application of quantum mechanical principles to a biological context in an adaptation of the polyene in a box concept. As part of the learner journey, they gain experience of practical computational chemistry, which provided an in silico alternative to traditional laboratory work during the SARS‐CoV‐19 pandemic. Student feedback was overwhelmingly positive, and this approach is now firmly embedded in the undergraduate curriculum. [ABSTRACT FROM AUTHOR]

WaveTrain is an open-source software for numerical simulations of chain-like quantum systems with nearest-neighbor (NN) interactions only. The Python package is centered around tensor train (TT, or matrix product) format representations of Hamiltonian operators and (stationary or time-evolving) state vectors. It builds on the Python tensor train toolbox Scikit_tt, which provides efficient construction methods and storage schemes for the TT format. Its solvers for eigenvalue problems and linear differential equations are used in WaveTrain for the time-independent and time-dependent Schrödinger equations, respectively. Employing efficient decompositions to construct low-rank representations, the tensor-train ranks of state vectors are often found to depend only marginally on the chain length N. This results in the computational effort growing only slightly more than linearly with N, thus mitigating the curse of dimensionality. As a complement to the classes for full quantum mechanics, WaveTrain also contains classes for fully classical and mixed quantum–classical (Ehrenfest or mean field) dynamics of bipartite systems. The graphical capabilities allow visualization of quantum dynamics "on the fly," with a choice of several different representations based on reduced density matrices. Even though developed for treating quasi-one-dimensional excitonic energy transport in molecular solids or conjugated organic polymers, including coupling to phonons, WaveTrain can be used for any kind of chain-like quantum systems, with or without periodic boundary conditions and with NN interactions only. The present work describes version 1.0 of our WaveTrain software, based on version 1.2 of scikit_tt, both of which are freely available from the GitHub platform where they will also be further developed. Moreover, WaveTrain is mirrored at SourceForge, within the framework of the WavePacket project for numerical quantum dynamics. Worked-out demonstration examples with complete input and output, including animated graphics, are available. [ABSTRACT FROM AUTHOR]

David Wallace's 'Dennett's Criterion' plays a key part in establishing realist claims about the existence of a multiverse emerging from the mathematical formalism of quantum physics, even after decoherence is fully appreciated. Although the philosophical preconditions of this criterion are not neutral, they are rarely explicitly addressed conceptually. I tease apart three: (I) a rejection of conceptual bridge laws even in cases of inhomogeneous reduction; (II) a reliance on the pragmatic notion of usefulness to highlight quasi-classical patterns, as seen in a decoherence basis, over others; and (III) a structural realist or 'functional realist' point of view that leads to individuating those patterns as real macroscopic objects at the coarse-grained level, as they are seen from the Classical Stance (analogous to Dennett's Intentional Stance). I conclude that the justification of Dennett's Criterion will be intimately tied up with the fate of strong forms of naturalism, and in particular that Wallacian quantum mechanics is a key case study for concretely evaluating his 'math-first' structural realism (Wallace 2022). [ABSTRACT FROM AUTHOR]

Projective quantum measurement is a theoretically accepted process in modern quantum mechanics. However, its projection hypothesis is widely regarded as an experimentally established empirical law. In this paper, we combine a previous result regarding the realization of a Hamiltonian process of the projection hypothesis in projective quantum measurement, where the complete set of the orbital observables of the center of mass of a macroscopic quantum mechanical system is restricted to a set of mutually commuting classical observables, and a previous result regarding the work required for an event reading (i.e. the informatical process in projective quantum measurement). Then, a quantum thermodynamic scheme is proposed for experimentally testing these two mutually independent theoretical results of projective quantum measurement simultaneously. [ABSTRACT FROM AUTHOR]

Quantum coherence constitutes a foundational characteristic of quantum mechanics and is integral to emerging quantum resource theories. However, quantum coherence is severely restricted by environmental noise in general quantum processing, indicated by the loss of information of a quantum system. Such processing can be described by the trade-offs between the coherence and the mixedness. Based on the l 2 norm coherence, conditional von Neumann entropy and Wigner–Yanase skew information, we derive basis-independent constraints on the attainable quantum coherence imposed by the mixedness of a quantum state, which generalize the prior basis-dependent relations, provide fundamental insights into the latent coherence resources present within arbitrary quantum systems that undergo decoherence and quantify the inherent limits on extractable coherence imposed by environmental noise. [ABSTRACT FROM AUTHOR]

We develop a version of quantum mechanics that can handle nonassociative algebras of observables and which reduces to standard quantum theory in the traditional associative setting. Our algebraic approach is naturally probabilistic and is based on using the universal enveloping algebra of a general nonassociative algebra to introduce a generalized notion of associative composition product. We formulate properties of states together with notions of trace, and use them to develop Gel'fand–Naimark–Segal constructions. We describe Heisenberg and Schrödinger pictures of completely positive dynamics, and we illustrate our formalism on the explicit examples of finite-dimensional matrix Jordan algebras as well as the octonion algebra. [ABSTRACT FROM AUTHOR]

This paper focuses on absolute spontaneity, first postulated by Immanuel Kant. In the early twentieth century spontaneity entered the domain of quantum physics when Niels Bohr included it as part of his quantum postulate. Later on, David Bohm developed the concept of a quantum potential in his description and interpretation of quantum physics, a concept that can also be understood in terms of spontaneity. A discussion of Kant's influence on the interpretation of quantum physics is followed by a consideration of the inclusion of spontaneity in Niels Bohr's epistemological approach to quantum mechanics and David Bohm's quantum potential as part of his ontological approach to quantum physics. Kant's influence on both Bohr and Bohm is examined as well as the applicability of his critical metaphysics to quantum theory. Critical metaphysics read together with Bohr and Bohm's interpretations of quantum physics is then utilized to make some proposals with regard to the problems plaguing our best theories of physics. [ABSTRACT FROM AUTHOR]

This paper explains how the so-called Einstein locality is to be understood in the Schrödinger picture of quantum mechanics. This notion is fully compatible with the Bell non-locality exhibited by entangled states. Contrary to the belief that quantum mechanics is incomplete, it is, As a matter of fact, its overcompleteness, as exemplified by the different pictures of quantum physics, that points to the same underlying reality. [ABSTRACT FROM AUTHOR]

Nonlinear mean field dynamics enables quantum information processing operations that are impossible in linear one‐particle quantum mechanics. In this approach, a register of bosonic qubits (such as neutral atoms or polaritons) is initialized into a symmetric product state |ψ⟩⊗n$| \psi \rangle ^{ \! \otimes n }$ through condensation, then subsequently controlled by varying the qubit‐qubit interaction. An experimental implementation of quantum state discrimination, an important subroutine in quantum computation, with a toroidal Bose–Einstein condensate is proposed. The condensed bosons here are atoms, each in the same superposition of angular momenta 0 and ℏ$\hbar$, encoding a qubit. A nice feature of the protocol is that only a readout of individual quantized circulation states (not superpositions) is required. [ABSTRACT FROM AUTHOR]

The exploration of pseudo-Hermitian quantum mechanics has led to rapid progress in the methods of constructing inner products and determining the observables of the theory in quantum sciences. In this paper, we introduce metric controlled operator-valued frames and our motivation is to find the applications in the generalized setting of quantum mechanics. We give various characterizations of metric controlled operator-valued frames. We also explore various spectral properties of pseudo-Hermitian and pseudo-unitary operators. Finally, we give the method of representing infinte quantum channels in pseudo-Hermitian quantum mechanics using metric controlled operator-valued frames. [ABSTRACT FROM AUTHOR]

This paper studies the notion of virtuality in the Bohr-Kramers-Slater theory of 1924. We situate the virtual entities of BKS within the tradition of the correspondence principle and the radiation theory of the Bohr model. We show how, in this context, virtual oscillators emerged as classical substitute radiators and were used to describe the otherwise elusive quantum transitions. They played an effective role in the quantum theory of radiation while remaining categorically distinct and ontologically separated from the quantum world of the Bohr model. The notion of virtuality thus differs markedly from its counterpart in quantum mechanics or QFT. [ABSTRACT FROM AUTHOR]

Quantum mechanics has withstood every experimental test thus far. However, it relies on ad-hoc postulates which require experimental verification. Over the past decade there has been a great deal of research testing these postulates, with numerous tests of Born's rule for determining probabilities and the complex nature of the Hilbert space being carried out. Although these tests are yet to reveal any significant deviation from textbook quantum theory, it remains important to conduct such tests in different configurations and using different quantum states. Here we perform the first such test using coherent states of light in a three-arm interferometer combined with homodyne detection. Our proposed configuration requires additional assumptions, but importantly allows us to use quantum states which exist in a larger Hilbert space compared to previous tests. For testing Born's rule, we find that the third order interference is bounded to be κ = 0.002 ± 0.004 and for testing whether quantum mechanics is complex or not we find a Peres parameter of F = 1.0000 ± 0.0003 (F = 1 corresponds to the expected complex quantum mechanics). We also design and implement a test of Glauber's theory of optical coherence. [ABSTRACT FROM AUTHOR]

The Born rule is part of the collapse axioms in the standard version of quantum theory, as presented by most textbooks on the subject. We show here that its signature quadratic dependence on the initial wavefunction's projection onto the measured outcome state follows from a single additional assumption beyond the other axioms. We give two examples of such an assumption, with a separate derivation for each, and we discuss their relationship with existing derivations. Our presentation is suitable for advanced undergraduates or graduate students who have taken a standard course in quantum theory. It does not depend on any particular interpretation of the theory. The Born rule predicts the probability of the outcome of a measurement on a quantum system, which depends on the projection of the initial state onto the eigenstates of the observable operator. This article shows that the Born rule can be derived from the other axioms of quantum mechanics theory by assuming non-contextuality: the probability of the outcome only depends on the final observed eigenstate. These derivations do not assume any particular interpretation of the theory and could be used as an exercise for undergraduate or graduate students studying the foundations of quantum mechanics. [ABSTRACT FROM AUTHOR]

This article reconsiders E. Schrödinger's cat paradox experiment from a new perspective, grounded in the interpretation of quantum mechanics that belongs to the class of interpretations designated as "reality without realism" (RWR) interpretations. These interpretations assume that the reality ultimately responsible for quantum phenomena is beyond conception, an assumption designated as the Heisenberg postulate. Accordingly, in these interpretations, quantum physics is understood in terms of the relationships between what is thinkable and what is unthinkable, with, physical, classical, and quantum, corresponding to thinkable and unthinkable, respectively. The role of classical physics becomes unavoidable in quantum physics, the circumstance designated as the Bohr postulate, which restores to classical physics its position as part of fundamental physics, a position commonly reserved for quantum physics and relativity. This view of quantum physics and relativity is maintained by this article as well but is argued to be sufficient for understanding fundamental physics. Establishing this role of classical physics is a distinctive contribution of the article, which allows it to reconsider Schrödinger's cat experiment, but has a broader significance for understanding fundamental physics. RWR interpretations have not been previously applied to the cat experiment, including by N. Bohr, whose interpretation, in its ultimate form (he changed it a few times), was an RWR interpretation. The interpretation adopted in this article follows Bohr's interpretation, based on the Heisenberg and Bohr postulates, but it adds the Dirac postulate, stating that the concept of a quantum object only applies at the time of observation and not independently. [ABSTRACT FROM AUTHOR]

The problem of quantum measurement can be partially resolved by incorporating a process of spontaneous disentanglement into quantum dynamics. A modified master equation is proposed, which contains a nonlinear term giving rise to both spontaneous disentanglement and thermalization. It is found that the added nonlinear term enables limit cycle steady states, which are prohibited in standard quantum mechanics. This finding suggests that an experimental observation of such a limit cycle steady state can provide an important evidence supporting the spontaneous disentanglement hypothesis. [ABSTRACT FROM AUTHOR]

It is aimed to study a hybrid quantum‐classical system in which a qubit as a quantum system coupled to a semi‐infinite 1D photonic crystal (PC) waveguide, and is controlled by a classical driving field. PC waveguides with engineering capability serve as engineered reservoirs where various manifestations of quantum mechanics can be studied. Here, the main purpose of the study is to evaluate the effect of coherent control on the dynamics of quantum Fisher information (QFI) and geometric phase (GP). It is revealed that the intensity (the Rabi frequency) of the classical field, memory time, and geometric length of the waveguide are key variables whose judicious choice aids in optimizing the estimation of the quantum parameters that are initially encoded in the qubit state. It is observed that the optical length of the waveguide and the Rabi frequency of the classical field have an interplay effect on the dynamic of the QFI and geometric phase. As an interesting finding, it is disclosed that as the Rabi frequency increases, the effect of the optical length of the waveguide fades away, and the Rabi frequency solely controls the geometric phase. Moreover, it is demonstrated that the estimation accuracy increases as the memory time decreases. On the other hand, lengthening the memory time lessens the dependency of the geometric phase on the length of the waveguide. [ABSTRACT FROM AUTHOR]

I identify and characterize a type of noncausal explanation in physics. I first introduce a distinction, between the physical properties of a system, and the representational properties of the mathematical expressions of the system's physical properties. Then I introduce a novel kind of property, which I shall call a dual property. This is a special kind of representational property, one for which there is an interpretation as a physical property. It is these dual properties that, I claim, are amenable to noncausal (mathematical, in fact) explanations. I discuss a typical example of such a dual property, and an example of an explanation as to why that dual property holds (the explanation of the quantization of the linear momentum). [ABSTRACT FROM AUTHOR]

In their recent articles Gruber, Block and Montemayor (2022: Front. Psychol., 13 , 718505) and Buonomano and Rovelli (2022: arXiv:2110.01976) discuss the differences between time in physics and psychology. With the aim of commenting on their views, we first outline a few general aspects of relativity theory, and some of the core elements of our approach, referring the reader to Aerts (1996: Found. Phys., 26 , 1627–1644; 2018: Found. Sci., 23 , 511–547), Aerts and Aerts (2004: in A. C. Elitzur, S. Dolev and N. Kolenda (Eds), Quo Vadis Quantum Mechanics? Possible Developments in Quantum Theory in the 21 st Century , pp. 153–207) and Aerts and Sassoli de Bianchi (2023: arXiv:2307.04764) for more details. In our approach, the ability of the experimenter to freely choose to perform or not to perform an experiment is explicitly considered and applied to the typical twin-paradox situation. This leads to the definition of a four-dimensional spacetime reality for each observer, a personal block universe. This is compatible with the existence of a local contextual present for each observer, travelling on their worldline, from their personal past to their personal future. Global spacetime becomes, as a corollary, a structure full of measurement-induced bifurcations towards the future, thus fundamentally nondeterministic. We analyze and highlight how this nondeterministic global reality is the one that follows from an operational approach inspired by quantum foundations, opening a way for an integration of relativity and quantum. [ABSTRACT FROM AUTHOR]

In this paper, I present a new analysis of the meaning of the phase in quantum mechanics. First, I give a simple but rigorous proof that the global phase is not real in ψ -ontic quantum theories. Next, I argue that a similar strategy cannot be used to prove the reality of the global phase due to the existence of the tails of the wave function. Finally, I argue that the relative phase is not a nonlocal property of two regions together, and adding a relative phase to one local branch of a superposition only changes the local properties at the boundary of the region of the branch. [ABSTRACT FROM AUTHOR]

At the onset of quantum mechanics, it was argued that the new theory would entail a rejection of classical logic. The main arguments to support this claim come from the non-commutativity of quantum observables, which allegedly would generate a non-distributive lattice of propositions, and from quantum superpositions, which would entail new rules for quantum disjunctions. While the quantum logic program is not as popular as it once was, a crucial question remains unsettled: what is the relationship between the logical structures of classical and quantum mechanics? In this essay we answer this question by showing that the original arguments promoting quantum logic contain serious flaws, and that quantum theory does satisfy the classical distributivity law once the full meaning of quantum propositions is properly taken into account. Moreover, we show that quantum mechanics can generate a distributive lattice of propositions, which, unlike the one of quantum logic, includes statements about expectation values which are of undoubtable physical interest. Lastly, we show that the lattice of statistical propositions in classical mechanics follows the same structure, yielding an analogue non-commutative sublattice of classical propositions. This fact entails that the purported difference between classical and quantum logic stems from a misconstructed parallel between the two theories. [ABSTRACT FROM AUTHOR]

Non-Hermitian Hamiltonians provide an alternative perspective on the dynamics of quantum and classical systems coupled non-conservatively to an environment. Once primarily an interest of mathematical physicists, the theory of non-Hermitian Hamiltonians has solidified and expanded to describe various physically observable phenomena in optical, photonic, and condensed matter systems. Self-consistent descriptions of quantum mechanics based on non-Hermitian Hamiltonians have been developed and continue to be refined. In particular, non-Hermitian frameworks to describe magnonic and hybrid magnonic systems have gained popularity and utility in recent years with new insights into the magnon topology, transport properties, and phase transitions coming into view. Magnonic systems are in many ways a natural platform in which to realize non-Hermitian physics because they are always coupled to a surrounding environment and exhibit lossy dynamics. In this Perspective, we review recent progress in non-Hermitian frameworks to describe magnonic and hybrid magnonic systems, such as cavity magnonic systems and magnon–qubit coupling schemes. We discuss progress in understanding the dynamics of inherently lossy magnetic systems as well as systems with gain induced by externally applied spin currents. We enumerate phenomena observed in both purely magnonic and hybrid magnonic systems which can be understood through the lens of non-Hermitian physics, such as P T and anti- P T -symmetry breaking, dynamical magnetic phase transitions, non-Hermitian skin effect, and the realization of exceptional points and surfaces. Finally, we comment on some open problems in the field and discuss areas for further exploration. [ABSTRACT FROM AUTHOR]

The vibrational spectra of condensed and gas-phase systems are influenced by thequantum-mechanical behavior of light nuclei. Full-dimensional simulations of approximate quantum dynamics are possible thanks to the imaginary time path-integral (PI) formulation of quantum statistical mechanics, albeit at a high computational cost which increases sharply with decreasing temperature. By leveraging advances in machine-learned coarse-graining, we develop a PI method with the reduced computational cost of a classical simulation. We also propose a simple temperature elevation scheme to significantly attenuate the artifacts of standard PI approaches as well as eliminate the unfavorable temperature scaling of the computational cost. We illustrate the approach, by calculating vibrational spectra using standard models of water molecules and bulk water, demonstrating significant computational savings and dramatically improved accuracy compared to more expensive reference approaches. Our simple, efficient, and accurate method has prospects for routine calculations of vibrational spectra for a wide range of molecular systems - with an explicit treatment of the quantum nature of nuclei. [ABSTRACT FROM AUTHOR]

Einstein–Podolsky–Rosen (EPR) paradox highlights the absence of a local realistic explanation for quantum mechanics, and shows the incompatibility of the local-hidden-state models with quantum theory. For N-qubit states, or more importantly, the N-qubit mixed states, we present the EPR steering paradox in the form of the contradictory equality " 2 = 1 ". We show that the contradiction holds for any N-qubit state as long as both "the pure state requirement" and "the measurement requirement" are satisfied. This also indicates that the EPR steering paradox exists in more general cases. Finally, we give specific examples to demonstrate and analyze our arguments. [ABSTRACT FROM AUTHOR]

Whether or not quantum physics can account for molecular structure is a matter of considerable controversy. Three of the problems raised in this regard are the problems of molecular structure. We argue that these problems are just special cases of the measurement problem of quantum mechanics: insofar as the measurement problem is solved, the problems of molecular structure are resolved as well. In addition, we explore one consequence of our argument: that claims about the reduction or emergence of molecular structure cannot be settled independently of the choice of a particular resolution to the measurement problem. Specifically, we consider how three standard putative solutions to the measurement problem inform our understanding of a molecule in isolation, as well as of chemistry's relation to quantum physics. [ABSTRACT FROM AUTHOR]

We analyzed the propagation of an incident electromagnetic wave in a purely-time modulated medium. Precisely, we assumed that the permeability is unchanged while the permittivity has a multiple-step profile in time and is uniformly constant in space. For this, we used the time-dispersive Drude's model with time-dependent plasma frequency and highly concentrated values near the centers of the steps' intervals. Under certain regimes, linking the number of steps to the contrasts of the permittivity, we can generate effective permittivity having positive and high values on a finite interval of time which behaves as a 'wall' that kills the forward waves and keeps only the backward waves (i.e. enabling full reflection). But, this happens if these high values are away from a discrete set. If these high values are close to the elements of this discrete set, then the effective medium behaves as a 'well' that absorbs all the forward waves and hence there are no backward waves (i.e. enabling full transmission). Such results are reminiscent to the 'wall' and 'well' effects known in the quantum mechanics theory. [ABSTRACT FROM AUTHOR]

The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of partitions. Or, putting it the other way around, the math of partitions is a skeletal version of the math of QM. The key concepts throughout this progression from logic, to logical information, to quantum theory are distinctions versus indistinctions, definiteness versus indefiniteness, or distinguishability versus indistinguishability. The distinctions of a partition are the ordered pairs of elements from the underlying set that are in different blocks of the partition and logical entropy is defined (initially) as the normalized number of distinctions. The cognate notions of definiteness and distinguishability run throughout the math of QM, e.g., in the key non-classical notion of superposition (=ontic indefiniteness) and in the Feynman rules for adding amplitudes (indistinguishable alternatives) versus adding probabilities (distinguishable alternatives). [ABSTRACT FROM AUTHOR]

The study of supersymmetric quantum theory of superconductivity has been undertaken in a broader sense. The main features of supersymmetric quantum mechanics have been derived in a straightforward manner and the consequences of supersymmetric breaking have been analyzed in terms of the possibility of occurrence of superconductivity, dual superconductivity and color superconductivity. [ABSTRACT FROM AUTHOR]

The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum optomechanics and quantum computing have a highly nonlinear nature, which makes their analysis extraordinarily difficult using classical schemes. Typically, modern quantum systems of interest nowadays come with four basic properties: (i) quantumness, (ii) openness, (iii) randomness, and (iv) nonlinearity. The newly introduced method of higher-order operators targets analytical solutions to such systems, and while providing at least mathematically approximate expressions with improved accuracy over the fully linearized schemes, some cases admit exact solutions. Many different applications of this method in quantum and classically nonlinear systems are demonstrated throughout. This review is purposed to provide the reader with ease of access to this recent and well-established operator algebra, while going over a moderate amount of literature review. The reader with basic knowledge of quantum mechanics and quantum noise theory should be able to start using this scheme to his or her own problem of interest. [ABSTRACT FROM AUTHOR]

The present survey results from the will to reconcile two approaches to quantum probabilities: one rather physical and coming directly from quantum mechanics, the other more algebraic. The second leading idea is to provide a unified picture introducing jointly to several fields of applications, some of which are probably not familiar (at least in the form we present them) to the readers. Lastly, we take the opportunity to present various results obtained recently that use group and bialgebra techniques to handle notions such as cumulants or Wick polynomials in the various noncommutative probability theories. [ABSTRACT FROM AUTHOR]

Ideas and results in the quantum theory of experiments are reviewed. To fix ideas, a concrete example of indirect measurements, an experiment devised by Guerlin et al. (Nature 448(7156):889–893, 2007), and theoretical interpretations thereof (Bauer and Bernard, Phys Rev A 84(4):044103, 2011; Bauer et al., Ann H Poincaré 14:639–679, 2013) are recalled. Subsequently two important elements of the Copenhagen interpretation of quantum mechanics, viz. the von Neumann- and the Lüders measurement postulates, are recalled and rendered more precise. Next, a model originally proposed by Gisin et al. (Phys Rev Lett 52:1657–1660, 1984) is described and shown to imply these postulates. It is then used to provide a theoretical description of the experiment in Guerlin et al. (Nature 448(7156):889–893, 2007) involving a "Heisenberg cut" differing from the one invoked in (Bauer and Bernard, Phys Rev A 84(4):044103, 2011; Bauer et al., Ann H Poincaré 14:639–679, 2013; J Stat Phys 162:924–958, 2016). Some technical issues in the analysis of Gisin's model are elaborated upon. The paper concludes with remarks on a general principle that implies a universal law governing the stochastic time evolution of states of individual physical systems featuring events and leading to a solution of the so-called measurement problem in quantum mechanics. [ABSTRACT FROM AUTHOR]

Superdeterminism—where the Measurement Independence assumption in Bell's Theorem is violated—is frequently assumed to imply implausibly conspiratorial correlations between properties λ of particles being measured and measurement settings x and y. But it does not have to be so: a superdeterministic but non-conspiratorial locally causal model is developed where each pair of entangled particles has unique λ. The model is based on a specific but arbitrarily fine discretisation of complex Hilbert space, where λ defines the information, over and above the freely chosen nominal settings x and y, which fixes the exact measurement settings X and Y of a run of a Bell experiment. Pearlean interventions, needed to assess whether x and y are Bell-type free variables, are shown to be inconsistent with rational-number constraints on the discretised Hilbert states. These constraints limit the post-hoc freedom to vary x keeping λ and y fixed but disappear with any coarse-graining of λ , X, and Y, rendering so-called drug-trial conspiracies irrelevant. Points in the discretised space can be realised as ensembles of symbolically labelled deterministic trajectories on an 'all-at-once' fractal attractor. It is shown how quantum mechanics might be 'gloriously explained and derived' as the singular continuum limit of the discretisation of Hilbert space. It is argued that the real message behind Bell's Theorem has less to do with locality, realism, or freedom to choose, and more to do with the need to develop more explicitly holistic theories when attempting to synthesise quantum and gravitational physics. [ABSTRACT FROM AUTHOR]

Combining gravity with quantum theory is still a work in progress. On the one hand, classical gravity is the geometry of space-time determined by the energy–momentum tensor of matter and the resulting nonlinear equations; on the other hand, the mathematical description of a quantum system is Hilbert space with linear equations describing evolution. In this paper, various measures in Hilbert space will be presented. In general, distance measures in Hilbert space can be divided into measures determined by energy and measures determined by entropy. Entropy measures determine quasi-distance because they do not satisfy all the axioms defining distance. Finding a general rule to determine such a measure unambiguously seems to be fundamental. [ABSTRACT FROM AUTHOR]