We point out a correspondence between classical and quantum states, by showing that for every classical distribution over phase--space, one can construct a corresponding quantum state, such that in the classical limit of $\hbar\to 0$ the latter converges to the former with respect to all measurable quantities.
The investigation of quantum-classical correspondence may lead to gain a deeper understanding of the classical limit of quantum theory. We develop a quantum formalism on the basis of a linear-invariant theorem, which gives an exact quantum-classical correspondence for damped oscillatory systems that are perturbed by an arbitrary force. Within our formalism, the quantum trajectory and expectation values of quantum observables are precisely coincide with their classical counterparts in the case where we remove the global quantum constant h from their quantum results. In particular, we illustrate…
Position-dependent mass harmonic oscillator: classical-quantum mechanical correspondence and ordering-ambiguity
我们回收克鲁兹等人。的（Phys. Lett. A 369（2007）400）在经典和量子位置相关质量（PDM）振荡器上的工作。为了详细说明有序的模糊性，我们适当地修改了他们工作中报道的一些结果，并讨论了PDM谐振子的经典和量子力学对应。我们使用一个点正则变换，并证明了一个唯一的量子PDM振子哈密顿量（因此，一个唯一的有序模糊参数集j=l=-1/4和k=-1/2）。为了表明这样的参数集不仅仅是量子PDM振子哈密顿量的表现形式，我们考虑准自由PDM粒子在其自身PDM力场的影响下运动的经典和量子力学对应。
Quantum-to-classical correspondence in Krylov complexity
Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales（布宜诺斯艾利斯大学，理学院）；CONICET - Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA)（阿根廷国家科学研究委员会-布宜诺斯艾利斯大学，布宜诺斯艾利斯物理研究所）
We consider the scaling of entanglement entropy in random Projected Entangled Pairs States (PEPS) with an internal symmetry given by a finite group G. We systematically demonstrate a correspondence between this entanglement entropy and the difference of free energies of a classical Ising model with an addition non-local term. This non-local term counts the number of domain walls in a particular configuration of the classical spin model. We argue that for that overwhelming majority of such states, this gives rise to an area law scaling with well-defined topological entanglement entropy. The top…
The equilibrium properties of nanoscale systems can deviate significantly from standard thermodynamics due to their coupling to an environment. For the generalised $θ$-angled spin-boson model, we first derive a compact and general form of the classical equilibrium state including environmental corrections to all orders. Secondly, for the quantum spin-boson model we prove, by carefully taking a large spin limit, that Bohr's quantum-classical correspondence persists at all coupling strengths. This correspondence gives insight into the conditions for a coupled quantum spin to be well-approximated…
We show that the correspondence between quantum and classical mechanics can be tuned by varying the coupling strength between the cavity modes and an atom or a molecule. In the acceleration gauge the cavity-matter system is represented by an effective Hamiltonian with a non-trivial coupling appearing in the potential, and a renormaized mass. Importantly, the acceleration-gauge coupling is non-monotonic with the strength cavity-matter interaction. As a result one obtain effective approximately decoupled field-matter dynamics for weak and strong interactions. In the weak coupling regime the effe…
Unambiguous quantization from the maximum classical correspondence that is self-consistent: the slightly stronger canonical commutation rule Dirac missed
We consider the problem of quantum-classical correspondence in integrable field theories. We propose a method to construct a field theoretical coherent state, in which the expectation value of the quantum field operator exactly coincides with the classical soliton. We also discuss the time evolution of this quantum state and the instability due to the nonlinearity.
We in this paper demonstrate that the $PT$-symmetric non-Hermitian Hamiltonian for a periodically driven system can be generated from a kernel Hamiltonian by a generalized gauge transformation. The kernel Hamiltonian is Hermitian and static, while the time-dependent transformation operator has to be $PT$ symmetric and non-unitary in general. Biorthogonal sets of eigenstates appear necessarily as a consequence of non-Hermitian Hamiltonian. We obtain analytically the wave functions and associated non-adiabatic Berry phase $γ_{n}$ for the $n$th eigenstate. The classical version of the non-Hermiti…
Classical and quantum mechanics across representations: an operational reading of the Wigner Weyl correspondence
University of Vienna, Faculty of Physics（维也纳大学物理学院）；Vienna Center for Quantum Science and Technology（维也纳量子科学与技术中心）；Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences（奥地利科学院量子光学与量子信息研究所）；Constructor University（Constructor大学）；University of Geneva, Group of Applied Physics（日内瓦大学应用物理组）
Quantum-Classical Correspondence Principle for Work Distributions in a Chaotic System
我们用数值方法研究了混沌系统中的功分布，考察了量子功和经典功之间的关系。数值结果表明，在混沌系统中，量子功分布与经典功分布之间存在着对应原理。在最近的工作[Jarzynski，Quan，and Rahav，Phys. Rev. X 5，031038（2015）]中证明了一维（1D）可积系统的这种对应关系。我们的研究通过两点能量测量进一步证明了量子功的定义。
We work in the Heisenberg picture to demonstrate the classical-quantum correspondence (CQC) in which the dynamics of a quantum variable is equivalent to that of a complexified classical variable. The correspondence provides a tool for analyzing quantum backreaction problems which we illustrate by a toy model in which a rolling particle slows down due to quantum radiation. The dynamics found using the CQC is in excellent agreement with that found using the much more laborious full quantum analysis.
We map the quantum problem of a free bosonic field in a space-time dependent background into a classical problem. $N$ degrees of freedom of a real field in the quantum theory are mapped into $2N^2$ classical simple harmonic oscillators with specific initial conditions. We discuss how this classical-quantum correspondence (CQC) may be used to evaluate quantum radiation and fully treat the backreaction of quantum fields on classical backgrounds. The technique has widespread application, including to the quantum evaporation of classical breathers ("oscillons").
We study the quantum-classical correspondence of an experimentally accessible system of interacting bosons in a tilted triple-well potential. With the semiclassical analysis, we get a better understanding of the different phases of the quantum system and how they could be used for quantum information science. In the integrable limits, our analysis of the stationary points of the semiclassical Hamiltonian reveals critical points associated with second-order quantum phase transitions. In the nonintegrable domain, the system exhibits crossovers. Depending on the parameters and quantities, the qua…
