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To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R (t) ) representing another observable. In the language of physics, the information carried by R (t) ≠ R † (t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ (t) . From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ (t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the "kinematical input" operator R (t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a (t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R (t) mimicking the birth of the Universe ("Big Bang") at t = 0 . [ABSTRACT FROM AUTHOR]

Higher-spin diffeomorphisms are to higher-order differential operators what diffeomorphisms are to vector fields. Their rigorous definition is a challenging mathematical problem which might predate a better understanding of higher-spin symmetries and interactions. Several yes-go and no-go results on higher-spin diffeomorphisms are collected from the mathematical literature in order to propose a generalisation of the algebra of differential operators on which higher-spin diffeomorphisms are well-defined. This work is dedicated to the memory of Christiane Schomblond, who taught several generations of Belgian physicists the formative rigor and delicate beauty of theoretical physics. [ABSTRACT FROM AUTHOR]

We present a semiclassical quantization condition, i.e., quantum-classical correspondence, for steady states of nonadiabatic systems consisting of fast and slow degrees of freedom (DOFs) by extending Gutzwiller's trace formula to a nonadiabatic form. The quantum-classical correspondence indicates that a set of primitive hopping periodic orbits, which are invariant under time evolution in the phase space of the slow DOF, should be quantized. The semiclassical quantization is then applied to a simple nonadiabatic model and accurately reproduces exact quantum energy levels. In addition to the semiclassical quantization condition, we also discuss chaotic dynamics involved in the classical limit of nonadiabatic dynamics. [ABSTRACT FROM AUTHOR]

We show the procedure for the secondary quantization of the electromagnetic field in an inhomogeneous medium, based on the formalism of the scattering matrix. We demonstrate the electromagnetic field profiles, which are obtained as a result of applying the scattering matrix formalism and prove their orthogonality. Finally, we derive the Hamiltonian of the system. The obtained procedure allows us to use more complete representation of quantum theory in a layered medium to describe various effects in layered structures. [ABSTRACT FROM AUTHOR]

Abstract Recently, we have used a projection operator to fix the number of particles in a second quantization approach in order to deal with the canonical ensemble. Having been applied earlier to handle various problems in nuclear physics that involve fixed particle numbers, the projector formalism was extended to grant access as well to quantum-statistical averages in condensed matter physics, such as particle densities and correlation functions. In this light, the occupation numbers of the subsequent single-particle energy eigenstates are key quantities to be examined. The goal of this paper is (1) to provide a sound extension of the projector formalism directly addressing the occupation numbers as well as the chemical potential, and (2) to demonstrate how the emerging problems related to numerical instability for fermions can be resolved to obtain the canonical statistical quantities for both fermions and bosons. Highlights • Quantum canonical ensemble. • Bosons and fermions. • Projection operator. • Fock space. • Free energy, chemical potential, occupation numbers. [ABSTRACT FROM AUTHOR]

Following the lines of the recent papers (Daneshmand and Tavassoly, Int. J. Theor. Phys. 56, 1218 (2017)), we study quantum mechanical treatments of an interaction between a two-level atom with a single-mode field in the two-photon Jaynes-Cummings model, where the Hamiltonian of the field is considered to be the quantized Caldirola-Kanai (CK) Hamiltonian. As a result, we would expect that the quantum dynamics of the two-photon JCM in terms of the CK Hamiltonian is qualitatively different from that of the usual one-photon case. We analytically calculate the explicit form of the atom-field entangled state and numerically evaluate the dynamics of its physical properties. The degree of entanglement, atomic population as well as sub-Poissonian statistics and quadrature squeezing of the field are analyzed. We adjust the latter evolved parameters by appropriately tuning the damping parameter within the CK Hamiltonian and detuning factor. Finally, we report a field detuning asymmetry in the collective statistical behavior. [ABSTRACT FROM AUTHOR]

The functional Schrödinger representation of a scalar field on an n -dimensional static space-time background is argued to be a singular limiting case of the hypercomplex quantum theory of the same system obtained by the precanonical quantization based on the space-time symmetric De Donder–Weyl Hamiltonian theory. The functional Schrödinger representation emerges from the precanonical quantization when the ultraviolet parameter ϰ introduced by precanonical quantization is replaced by γ ̲ 0 δ inv (0) , where γ ̲ 0 is the time-like tangent space Dirac matrix and δ inv (0) is an invariant spatial (n − 1) -dimensional Dirac's delta function whose regularized value at x = 0 is identified with the cutoff of the volume of the momentum space. In this limiting case, the Schrödinger wave functional is expressed as the trace of the product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration and the canonical functional derivative Schrödinger equation is derived from the manifestly covariant Dirac-like precanonical Schrödinger equation which is independent of a choice of a codimension-one foliation. [ABSTRACT FROM AUTHOR]

Abstract A series of quantization identities are established for static vortex solutions governed by the Born–Infeld type actions. These identities are of a universal nature which are indifferent to the details of the models and provide refined descriptions of divergent energetic quantities. [ABSTRACT FROM AUTHOR]

Abstract Promoting recycling is one of the best effective measures to relieve contradictions such as “waste siege” and resource shortage in China. To do that, quantifying and recognizing the recycling potential (RCP) of recyclable waste (RCW) are foundations. This study quantifies the RCP of RCW (RCP-RCW) in Suzhou, a typical developed city in East China, based on a systematic tracking survey for one week in each season and in different districts starting from the summer of 2011 to the spring of 2017. Results show that Suzhou's RCP-RCW was 92.7 (89.3–96.0), with a 90% confidence interval percentage, among which, recyclable organics and recyclable material (RCM) accounted for 55.1% and 37.6%, respectively. In RCMs, a high RCM recovery value and low RCM recovery value accounted for 64.8% and 26.0%, respectively. RCW generation was 242.4 thousand tons in 2016 and is expected to reach 738.8 thousand tons in 2030. Moreover, spatiotemporal variation of RCW was characterized. Factors, such as local customs and culture, dietary habits, residential lifestyles and consumption structure influence the RCW stream generation. All the obtained results can improve the knowledge base for effectively promote recycling, and contribute to making governmental policy and the recycling industry's business development in Suzhou and other Chinese cities. Graphical abstract Image 1 Highlights • Recycling potential of recyclable waste (RCW) were quantitated. • RCWs generation trends were estimated. • Recommendations for recycling were proposed. [ABSTRACT FROM AUTHOR]

Structures and objects used in Hamiltonian secondary quantization are discussed. By the secondary quantization of a Hamiltonian system ℋ, we mean the Schrödinger quantization of another Hamiltonian system ℋ1 for which the Hamiltonian equation is the Schrödinger one obtained by the quantization of the original Hamiltonian system ℋ. The phase space of ℋ1 is the realification ℍR of the complex Hilbert space ℍ of the quantum analogue of ℋ equipped with the natural symplectic structure. The role of a configuration space is played by the maximal real subspace of ℍ. [ABSTRACT FROM AUTHOR]

In physics, one is often misled in thinking that the mathematical model of a system is part of or is that system itself. Think of expressions commonly used in physics like "point" particle, motion "on the line", "smooth" observables, wave function, and even "going to infinity", without forgetting perplexing phrases like "classical world" versus "quantum world".... On the other hand, when a mathematical model becomes really inoperative in regard with correct predictions, one is forced to replace it with a new one. It is precisely what happened with the emergence of quantum physics. Classical models were (progressively) superseded by quantum ones through quantization prescriptions. These procedures appear often as ad hoc recipes. In the present paper, well defined quantizations, based on integral calculus and Weyl-Heisenberg symmetry, are described in simple terms through one of the most basic examples of mechanics. Starting from (quasi-) probability distribution(s) on the Euclidean plane viewed as the phase space for the motion of a point particle on the line, i.e., its classical model, we will show how to build corresponding quantum model(s) and associated probabilities (e.g. Husimi) or quasi-probabilities (e.g. Wigner) distributions. We highlight the regularizing rôle of such procedures with the familiar example of the motion of a particle with a variable mass and submitted to a step potential. [ABSTRACT FROM AUTHOR]

Abstract We show a possibility for the charge quantization of the standard model (SM) particles. If a global symmetry makes the three copies of a generation and supersymmetry (SUSY) relates the Higgs boson to a lepton, all the charges of the SM particles can be quantized through gauge-anomaly cancellation. In the minimal model realizing the possibility, the gravitino mass around the Planck-scale is needed to generate the SM couplings through (quantum) supergravity. Much below the Planck-scale, the SM with non-vanishing neutrino masses is obtained as the effective theory. As extensions of the SM with this quantization mechanism, millicharged particles can exist without introducing massless hidden photons. [ABSTRACT FROM AUTHOR]

Abstract The concept of effective dynamics has proven successful in LQC, a loop-inspired quantization of cosmological spacetimes. We apply the same idea of its derivation in LQC to the full theory, by computing the expectation value of the scalar constraint with respect to some coherent states peaked on the phase-space variables of flat Robertson–Walker spacetime. We comment on the relation with effective LQC and find a deviation stemming from the Lorentzian part of the Hamiltonian. [ABSTRACT FROM AUTHOR]

It is often said that quantum and classical randomness are of different nature, the former being ontological and the latter epistemological. However, so far the question of 'What is quantum in quantum randomness?', i.e. what is the impact of quantization and discreteness on the nature of randomness, remains to be answered. In a first part, we make explicit the differences between quantum and classical randomness within a recently proposed ontology for quantum mechanics based on contextual objectivity. In this view, quantum randomness is the result of contextuality and quantization. We show that this approach strongly impacts the purposes of quantum theory as well as its areas of application. In particular, it challenges current programmes inspired by classical reductionism, aiming at the emergence of the classical world from a large number of quantum systems. In a second part, we analyse quantum physics and thermodynamics as theories of randomness, unveiling their mutual influences. We finally consider new technological applications of quantum randomness that have opened up in the emerging field of quantum thermodynamics. This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. [ABSTRACT FROM AUTHOR]

Quantum transport is studied for the nonequilibrium Anderson impurity model at zero temperature employing the multilayer multiconfiguration time-dependent Hartree theory within the second quantization representation (ML-MCTDH-SQR) of Fock space. To address both linear and nonlinear conductance in the Kondo regime, two new techniques of the ML-MCTDH-SQR simulation methodology are introduced: (i) the use of correlated initial states, which is achieved by imaginary time propagation of the overall Hamiltonian at zero voltage and (ii) the adoption of the logarithmic discretization of the electronic continuum. Employing the improved methodology, the signature of the Kondo effect is analyzed. [ABSTRACT FROM AUTHOR]

This article is an introductory presentation of the quantization of the half-plane based on affine coherent states (ACS). The half-plane carries a natural affine symmetry, i.e. it is a homogeneous space for the 1d-affine group, and it is viewed as the phase space for the dynamics of a positive physical quantity evolving with time. Its affine symmetry is preserved due to the covariance of this type of quantization. We promote the interest of such a procedure for transforming a classical model into a quantum one, since the singularity at the origin is systematically removed, and the arbitrariness of boundary conditions for the Schrödinger operator can be easily overcome. We explain some important mathematical aspects of the method. Three elementary examples of applications are presented, the quantum breathing of a massive sphere, the quantum smooth bouncing of a charged sphere, and a smooth bouncing of “dust” sphere as a simple model of quantum Newtonian cosmology. [ABSTRACT FROM AUTHOR]

We show that our recent Bohr-like approach to black hole (BH) quantum physics implies that spacetime quantization could be energy-dependent. Thus, in a certain sense, spacetime can be neither discrete nor continuous. Our approach also permits to show that the 'volume quantum' of the Schwarzschild spacetime increases with increasing energy during BH evaporation and arrives at a maximum value when the Planck scale is reached and the generalized uncertainty principle (GUP) prevents the total BH evaporation. Remarkably, this result does not depend on the BH original mass. The interesting consequence is that the behavior of BH evaporation should be the same for all Schwarzschild BHs when the Planck scale is approached. [ABSTRACT FROM AUTHOR]

The Wheeler-DeWitt equation was proposed 50 years ago and until now it is the cornerstone of most approaches to quantization of gravity. One can find in the literature, the opinion that the Wheeler-DeWitt equation is even more fundamental than the basic equation of quantum theory, the Schrödinger equation. We still should remember that we are in the situation when no observational data can confirm or reject the fundamental status of the Wheeler-DeWitt equation, so we can give just indirect arguments in favor of or against it, grounded on mathematical consistency and physical relevance. I shall present the analysis of the situation and comparison of the standard Wheeler-DeWitt approach with the extended phase space approach to quantization of gravity. In my analysis, I suppose, first, that a future quantum theory of gravity must be applicable to all phenomena from the early universe to quantum effects in strong gravitational fields, in the latter case, the state of the observer (the choice of a reference frame) may appear to be significant. Second, I suppose that the equation for the wave function of the universe must not be postulated but derived by means of a mathematically consistent procedure, which exists in path integral quantization. When applying this procedure to any gravitating system, one should take into account features of gravity, namely, nontrivial spacetime topology and possible absence of asymptotic states. The Schrödinger equation has been derived early for cosmological models with a finite number of degrees of freedom, and just recently it has been found for the spherically symmetric model which is a simplest model with an infinite number of degrees of freedom. The structure of the Schrödinger equation and its general solution appears to be very similar in these cases. The obtained results give grounds to say that the Schrödinger equation retains its fundamental meaning in constructing quantum theory of gravity. [ABSTRACT FROM AUTHOR]

The QCD light-front Hamiltonian equation HLFΨ=M2Ψ derived from quantization at fixed LF time τ=t  +  z/c provides a causal, frame-independent method for computing hadron spectroscopy as well as dynamical observables such as structure functions, transverse momentum distributions, and distribution amplitudes. The QCD Lagrangian with zero quark mass has no explicit mass scale. de Alfaro, Fubini, and Furlan (dAFF) have made an important observation that a mass scale can appear in the equations of motion without affecting the conformal invariance of the action if one adds a term to the Hamiltonian proportional to the dilatation operator or the special conformal operator. If one applies the dAFF procedure to the QCD light-front Hamiltonian, it leads to a color-confining potential κ4ζ2 for mesons, where ζ2 is the LF radial variable conjugate to the qq¯ invariant mass squared. The same result, including spin terms, is obtained using light-front holography, the duality between light-front dynamics and AdS5, if one modifies the AdS5 action by the dilaton eκ2z2 in the fifth dimension z. When one generalizes this procedure using superconformal algebra, the resulting light-front eigensolutions provide a unified Regge spectroscopy of meson, baryon, and tetraquarks, including remarkable supersymmetric relations between the masses of mesons and baryons and a universal Regge slope. The pion qq¯ eigenstate has zero mass at mq=0. The superconformal relations also can be extended to heavy-light quark mesons and baryons. This approach also leads to insights into the physics underlying hadronization at the amplitude level. I will also discuss the remarkable features of the Poincaré invariant, causal vacuum defined by light-front quantization and its impact on the interpretation of the cosmological constant. AdS/QCD also predicts the analytic form of the nonperturbative running coupling αs(Q2)∝e-Q2/4κ2. The mass scale κ underlying hadron masses can be connected to the parameter ΛMS¯ in the QCD running coupling by matching the nonperturbative dynamics to the perturbative QCD regime. The result is an effective coupling αs(Q2) defined at all momenta. One obtains empirically viable predictions for spacelike and timelike hadronic form factors, structure functions, distribution amplitudes, and transverse momentum distributions. Finally, I address the interesting question of whether the momentum sum rule is valid for nuclear structure functions. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the classical geometric flow as a dynamical system. We obtain an action for this system, such that its equation of motion is the Raychaudhuri equation. This action will be used to quantize this system. As the Raychaudhuri equation is the basis for deriving the singularity theorems, we will be able to understand the effects and such a quantization will have on the classical singularity theorems. Thus, quantizing the geometric flow, we can demonstrate that a quantum space-time is complete (nonsingular). This is because the existence of a conjugate point is a necessary condition for the occurrence of singularities, and we will be able to demonstrate that such conjugate points cannot occur due to such quantum effects. [ABSTRACT FROM AUTHOR]

We discuss a link between symplectic displacement energy, a fundamental notion of symplectic topology, and the quantum speed limit, a universal constraint on the speed of quantum-mechanical processes. The link is provided by the quantum-classical correspondence formalized within the framework of the Berezin-Toeplitz quantization. [ABSTRACT FROM AUTHOR]

Nearest neighbor search is a problem of finding the data points from the database such that the distances from them to the query point are the smallest. Learning to hash is one of the major solutions to this problem and has been widely studied recently. In this paper, we present a comprehensive survey of the learning to hash algorithms, categorize them according to the manners of preserving the similarities into: pairwise similarity preserving, multiwise similarity preserving, implicit similarity preserving, as well as quantization, and discuss their relations. We separate quantization from pairwise similarity preserving as the objective function is very different though quantization, as we show, can be derived from preserving the pairwise similarities. In addition, we present the evaluation protocols, and the general performance analysis, and point out that the quantization algorithms perform superiorly in terms of search accuracy, search time cost, and space cost. Finally, we introduce a few emerging topics. [ABSTRACT FROM PUBLISHER]

We develop a new method to study electrical circuits at quantum nanoscale by introducing a heat momentum operator which reproduces quantum effects similar to those obtained in Suykens's nonlocal-in-time kinetic energy approach for the case of reversible motion. The series expansion of the heat momentum operator is similar to the momentum operator obtained in the framework of minimal length phenomenologies characterized by the deformation of Heisenberg algebra. The quantization of both LC and mesoscopic circuits revealed a number of motivating features like the emergence of a generalized uncertainty relation and a minimal charge similar to those obtained in the framework of minimal length theories. Additional features were obtained and discussed accordingly. [ABSTRACT FROM AUTHOR]

We present the quantum theory of the Penning trap in terms of individualxandyradial modes of the motion of a single charged particle in the trap, and demonstrate how the conventional rotating frame used to examine these individual dynamics fails in the quantum regime. In solving the radial Hamiltonian in thebasis, we show how canonical transformation of the variables must take placeafterquantization, in order that these separate motions can be consistently tracked. This is in contrast to previous work. The results of the discussion lend themselves to a fully quantum treatment of mode coupling in the trap, leading to an avoided crossing between the coupled energy levels of the system. Exploiting the algebraic structure of the problem allows employment of a dressed-atom formalism within quantum Penning trap theory, and future applications resulting from this are proposed. [ABSTRACT FROM PUBLISHER]

In this series of papers, we investigate the projective framework initiated by Kijowski (1977) and Okołów (2009, 2014, 2013) [1,2] , which describes the states of a quantum theory as projective families of density matrices. A short reading guide to the series can be found in Lanéry (2016). A strategy to implement the dynamics in this formalism was presented in our first paper Lanéry and Thiemann (2017) (see also Lanéry, 2016, section 4), which we now test in two simple toy-models. The first one is a very basic linear model, meant as an illustration of the general procedure, and we will only discuss it at the classical level. In the second one, we reformulate the Schrödinger equation, treated as a classical field theory, within this projective framework, and proceed to its (non-relativistic) second quantization. We are then able to reproduce the physical content of the usual Fock quantization. [ABSTRACT FROM AUTHOR]

In this work we discuss the Yukawa model with the extra term of self-interacting scalar field in $$D=1+3$$ dimensions. We present the method of derivation the light-front commutators and anti-commutators from the Heisenberg equations induced by the kinematical generating operator of the translation $$P^{+}$$ . Mentioned Heisenberg equations are the starting point for obtaining this algebra of the (anti-) commutators. Some discrepancies between existing and proposed method of quantization are revealed. The Lorentz and the CPT symmetry, together with some features of the quantum theory were applied to obtain the two-point Wightman function for the free fermions. Moreover, these Wightman functions were computed especially without referring to the Fock expansion. The Gaussian effective potential for the Yukawa model was found in the terms of the Wightman functions. It was regularized by the space-like point-splitting method. The coupling constants within the model were redefined. The optimum mass parameters remained regularization independent. Finally, the Gaussian effective potential was renormalized. [ABSTRACT FROM AUTHOR]

In this paper, we give a correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the torus T2. To achieve this, we use the correspondence between the Berezin-Toeplitz and the complex Weyl quantizations of the complex plane and a relation between the Berezin-Toeplitz quantization of a periodic symbol on the real phase space R2 and the Berezin-Toeplitz quantization of a symbol on the torus T2. [ABSTRACT FROM AUTHOR]

Despite its age, quantum theory still suffers from serious conceptual difficulties. To create clarity, mathematical physicists have been attempting to formulate quantum theory geometrically and to find a rigorous method of quantization, but this has not resolved the problem. In this article we argue that a quantum theory recursing to quantization algorithms is necessarily incomplete. To provide an alternative approach, we show that the Schrödinger equation is a consequence of three partial differential equations governing the time evolution of a given probability density. These equations, discovered by Madelung, naturally ground the Schrödinger theory in Newtonian mechanics and Kolmogorovian probability theory. A variety of far-reaching consequences for the projection postulate, the correspondence principle, the measurement problem, the uncertainty principle, and the modeling of particle creation and annihilation are immediate. We also give a speculative interpretation of the equations following Bohm, Vigier and Tsekov, by claiming that quantum mechanical behavior is possibly caused by gravitational background noise. [ABSTRACT FROM AUTHOR]

The spectrum of masses of the colorless states of DW Hamiltonian operator of quantum SU(2) Yang-Mills field theory on obtained via the precanonical quantization is shown to be purely discrete and bounded from below. The scale of the mass gap is estimated to be of the order of magnitude of the scale of the ultra-violet parameter which is introduced by precanonical quantization on dimensional grounds. [ABSTRACT FROM AUTHOR]

The well-known trigonometric Scarf potential is generalized by adding a sinusoidal term and then treated using the Asymptotic Iteration Method (AIM) and the Tridiagonal Representation Approach (TRA). The energy spectrum of the associated bound states is computed. For the AIM, we have improved convergence of the quantization condition that terminates the iterations asymptotically. This is accomplished by looking for the range of initial values of the space variable in the terminating condition that produces stable results (plateau of convergence). We have shown that with increasing iteration, this plateau of convergence grows up rapidly to an optimal iteration number and then shrinks slowly to a point. The value of this point (or points) may depend on the physical parameters. The numerical results have been compared favorably with those resulting from the TRA. [ABSTRACT FROM AUTHOR]

We study quantum corrections to projectable Hořava gravity with z = 2 scaling in 2 + 1 dimensions. Using the background field method, we utilize a non-singular gauge to compute the anomalous dimension of the cosmological constant at one loop, in a normalization adapted to the spatial curvature term. [ABSTRACT FROM AUTHOR]

In addition to stable pulse generation, passively mode-locked fiber lasers can easily run into an unstable regime of multipulse mode-locking. The birth and dynamic behaviors of multipulse mode-locking so far have rarely been experimentally explored, particularly in the spectral domain. In this letter, several kinds of multipulse spectral-temporal dynamics of a passively mode-locked fiber laser are observed in a single-shot manner, e.g., energy quantization, self-phase modulation spectral broadening, wavelength shifting, spectral interfering, and ultraweak pulse interaction. This study is enabled by the high temporal resolution of spectral-temporal technology, i.e., 50 ps in the time domain and tens of nanoseconds in the spectral domain. Moreover, a wide observing time span of our spectral-temporal analyzing system, i.e., >6 ms—equivalent to 100 000 round trips, enables evolutionary characterization of individual pulses. The results will have a significant impact on optimizing the performance of mode-locked fiber lasers and understanding the nonlinear physics in a dissipative system. [ABSTRACT FROM AUTHOR]

According to quantum theory the energy exchange between physical systems is quantized. As a direct consequence, measurement sensitivities are fundamentally limited by quantization noise, or just ‘quantum noise’ in short. Furthermore, Heisenberg’s Uncertainty Principle demands measurement back-action for some observables of a system if they are measured repeatedly. In both respects, squeezed states are of high interest since they show a ‘squeezed’ uncertainty, which can be used to improve the sensitivity of measurement devices beyond the usual quantum noise limits including those impacted by quantum back-action noise. Squeezed states of light can be produced with nonlinear optics, and a large variety of proof-of-principle experiments were performed in past decades. As an actual application, squeezed light has now been used for several years to improve the measurement sensitivity of GEO 600 – a laser interferometer built for the detection of gravitational waves. Given this success, squeezed light is likely to significantly contribute to the new field of gravitational-wave astronomy. This Review revisits the concept of squeezed states and two-mode squeezed states of light, with a focus on experimental observations. The distinct properties of squeezed states displayed in quadrature phase-space as well as in the photon number representation are described. The role of the light’s quantum noise in laser interferometers is summarized and the actual application of squeezed states in these measurement devices is reviewed. [ABSTRACT FROM AUTHOR]

We investigate the entropy product formula for various gravitational instantons. We speculate that due to the mass-independent features of the said instatons they are universal as well as quantized. For isolated Euclidean Schwarzschild black hole, these properties simply fail. [ABSTRACT FROM AUTHOR]

By proceeding with the idea that the presence of physical (BRST invariant) extra factors in the path integral is equivalent to taking into account explicitly the arbitrariness in resolving the quantum master equation, we consider the field-antifield quantization procedure both with the Abelian and the non-Abelian gauge fixing. [ABSTRACT FROM AUTHOR]

The fault-tolerant control problem is investigated for a class of networked batch processes with actuator faults and external disturbances. A two-dimensional Fornasini-Marchesini (2D-FM) system with multirate sampling and quantization effects is introduced to model the networked batch processes, which may reflect the reality more closely. The aim of this paper is to design a dynamic output feedback controller such that the closed-loop system can achieve fault tolerance with the effect of actuator faults and satisfy the H∞ performance constraint for unknown external disturbances. By employing a combination of the Lyapunov stability analysis theory, lifting technique, and logarithmic quantization method, a networked iterative learning fault-tolerant control (NILFTC) scheme is first proposed, and some sufficient conditions are established for the existence of the desired dynamic output feedback controller. Finally, an example is exploited to illustrate the effectiveness of the developed method. [ABSTRACT FROM AUTHOR]

Generic higher derivative theories are believed to be fundamentally unphysical because they contain Ostrogradsky ghosts. We show that within complex classical mechanics it is possible to construct higher derivative theories that circumvent the Ostrogradsky theorem and have a real energy spectrum that is bounded from below. The complex theory can be canonically quantised. The resulting quantum theory does not suffer from the kinetic instability and maintains the usual probabilistic interpretation without violating the correspondence principle. As a proof of concept, we construct a class of stable interacting complex higher derivative theories and present a concrete example. This consistent and canonical framework allows us to analyse the previous attempts to avoid ghosts that use non-canonical quantisation schemes, such as the Lee–Wick theories, Dirac–Pauli quantisation or PT -symmetric quantum mechanics. The key to understand the would-be ghosts in any kinetically stable higher derivative theory is to accept the complex system behind it. [ABSTRACT FROM AUTHOR]

Energy of a black hole is usually quantized by invoking some area quantization scheme after expressing the energy in terms of the horizon area. However, in this approach one has to quantize the local and asymptotic energy of the black hole separately and the two results do not manifest any physical correspondence with each other. Here, as opposed to this practice, we find the unique energy spectrum of black holes by adopting a top-down approach. The physical links among the underlying quantum theory, statistical mechanics and thermodynamics of the black hole horizon play the central role in determining the energy spectrum. The energy spectrum that we obtain explicitly reveals the correspondence between asymptotic and local observations through the presence of the surface gravity of the horizon as a parameter in the spectrum, rather than being expressed as a function of area and consequently getting quantized in the usual approach. Thus, our result presents a new view as far as black hole energy quantization is concerned. The calculations are performed using the quantum geometric description of black hole horizons as laid down by loop quantum gravity. [ABSTRACT FROM AUTHOR]

We introduce exactly solvable quantum parametric oscillators, which are generalizations of the quantum problems related with the classical orthogonal polynomials of Hermite, Laguerre, and Jacobi type, introduced in the work of Büyüka, sık et al. [J. Math. Phys. 50, 072102 (2009)]. Quantization of these models with specific damping, frequency, and external forces is obtained using the Wei-Norman Lie algebraic approach. This determines the evolution operator exactly in terms of two linearly independent homogeneous solutions and a particular solution of the corresponding classical equation of motion. Then, time-evolution of wave functions and coherent states are found explicitly. Probability densities, expectation values, and uncertainty relations are evaluated and their properties are investigated under the influence of the external terms. [ABSTRACT FROM AUTHOR]

We study the evolution of a quantum discrete nonlinear Schrödinger (DNLS) system using as initial conditions coherent states corresponding to points in the vicinity of breather solutions of the classical system. We consider various examples of stable and unstable breathers and examine the distance between exactly evolved states and coherent states with parameters that evolve according to classical dynamics. Initial conditions near stable breathers and their vicinity are seen to lead to recurrences to small distances between the two evolving states. Similar recurrences are not observed for initial conditions near unstable breathers. [ABSTRACT FROM AUTHOR]

We discuss the quantization of non-ultralocal integrable models directly in the continuous case, using the example of the Alday–Arutyunov–Frolov model. We show that by treating fields as distributions and regularizing the operator product, it is possible to avoid all the singularities, and allow to obtain results consistent with perturbative calculations. We illustrate these results by considering the reduction to the massive free fermion model and extracting the quantum Hamiltonian as well as other conserved charges directly from the regularized trace identities. Moreover, we show that our regularization recovers Maillet's prescription in the classical limit. [ABSTRACT FROM AUTHOR]

We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized theta function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local $${{\mathbb{P}}^2}$$ , local $${{\mathbb{P}}^1 \times {\mathbb{P}}^1}$$ and local $${{\mathbb{F}}_1}$$ . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators. Physically, our results provide a non-perturbative formulation of topological strings on toric Calabi-Yau manifolds, in which the genus expansion emerges as a 't Hooft limit of the spectral traces. Since the spectral determinant is an entire function on moduli space, it leads to a background-independent formulation of the theory. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry. [ABSTRACT FROM AUTHOR]

For a unital completely positive map $${\Phi}$$ ('quantum channel') governing the time propagation of a quantum system, the Stinespring representation gives an enlarged system evolving unitarily. We argue that the Stinespring representations of each power $${\Phi^m}$$ of the single map together encode the structure of the original quantum channel and provide an interaction-dependent model for the bath. The same bath model gives a 'classical limit' at infinite time $${m\to\infty}$$ in the form of a noncommutative 'manifold' determined by the channel. In this way, a simplified analysis of the system can be performed by making the large- m approximation. These constructions are based on a noncommutative generalization of Berezin quantization. The latter is shown to involve very fundamental aspects of quantum-information theory, which are thereby put in a completely new light. [ABSTRACT FROM AUTHOR]

We reconsider the (non-relativistic) quantum theory of indistinguishable particles on the basis of Rieffel's notion of -algebraic ('strict') deformation quantization. Using this formalism, we relate the operator approach of Messiah and Greenberg (1964) to the configuration space approach pioneered by Souriau (1967), Laidlaw and DeWitt-Morette (1971), Leinaas and Myrheim (1977), and others. In dimension , the former yields bosons, fermions, and paraparticles, whereas the latter seems to leave room for bosons and fermions only, apparently contradicting the operator approach as far as the admissibility of parastatistics is concerned. To resolve this, we first prove that in the topologically non-trivial configuration spaces of the second approach are quantized by the algebras of observables of the first. Secondly, we show that the irreducible representations of the latter may be realized by vector bundle constructions, among which the line bundles recover the results of the second approach. Mathematically speaking, representations on higher-dimensional bundles (which define parastatistics) cannot be excluded, which render the configuration space approach incomplete. Physically, however, we show that the corresponding particle states may always be realized in terms of bosons and/or fermions with an unobserved internal degree of freedom (although based on non-relativistic quantum mechanics, this conclusion is analogous to the rigorous results of the Doplicher-Haag-Roberts analysis in algebraic quantum field theory, as well as to the heuristic arguments which led Gell-Mann and others to qcd (i.e. Quantum Chromodynamics)). [ABSTRACT FROM AUTHOR]

A hybrid distortion function for JPEG steganography exploiting block fluctuation and quantization steps is proposed. To resist multidomain steganalysis, both spatial domain and discrete cosine transformation (DCT) domain are involved in the proposed distortion function. In spatial domain, a distortion value is allotted for each 8 × 8 block according to block fluctuation. In DCT domain, quantization steps are employed to allot distortion values for DCT coefficients in a block. The two elements, block distortion and quantization steps, are combined together to measure the embedding risk. By employing the syndrome trellis coding to embed secret data, the embedding changes are constrained in complex regions, where modifications are hard to be detected. When compared to current state-of-the-art steganographic methods for JPEG images, the proposed method presents less detectable artifacts. ©2016 SPIE and IS&T [DOI: 10.1117/1.JEI.25.5.050501] [ABSTRACT FROM AUTHOR]

In this paper we study the third quantized super-group field cosmology, a model in multiverse scenario, in Batalin-Vilkovisky (BV) formulation. Further, we propose the superfield/super-antifield dependent BRST symmetry transformations. Within this formulation we establish connection between the two different solutions of the quantum master equation within the BV formulation. [ABSTRACT FROM AUTHOR]

The paper presents a program to construct a non-relativistic relational Bohmian theory, that is, a theory of N moving point-like particles that dispenses with space and time as fundamental background structures. The relational program proposed is based on the best-matching framework originally developed by Julian Barbour. In particular, the paper focuses on the conceptual problems that arise when trying to implement such a program. It is argued that pursuing a relational strategy in the Bohmian context leads to a more parsimonious ontology than that of standard Bohmian mechanics without betraying the original motivations for adopting a primitive ontology approach to quantum physics. It is also shown how a relational Bohmian approach might clarify the issue of the timelessness of the dynamics resulting from the quantization of a classical relational system of particles. [ABSTRACT FROM AUTHOR]

It is shown that the Dirac-Nambu-Goto brane can be described as a point particle in an infinite-dimensional brane space with a particular metric. This suggests a generalization to brane spaces with arbitrary metric, including the 'flat' metric. Then quantization of such a system is straightforward: it is just like quantization of a bunch of noninteracting particles. This leads us to a system of a continuous set of scalar fields. For a particular choice of the metric in the space of fields we find that the classical Dirac-Nambu-Goto brane theory arises as an effective theory of such an underlying quantum field theory. Quantization of branes is important for the brane world scenarios, and thus for 'quantum gravity.' [ABSTRACT FROM AUTHOR]