Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComplexity of quantum motion and quantum-classical correspondence: A phase-space approach
111
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We discuss the connection between the out-of-time-ordered correlator and the number of harmonics of the phase-space Wigner distribution function. In particular, we show that both quantities grow exponentially for chaotic dynamics, with a rate determined by the largest Lyapunov exponent of the underlying classical dynamics, and algebraically -- linearly or quadratically -- for integrable dynamics. It is then possible to use such quantities to detect in the time domain the integrability to chaos crossover in many-body quantum systems.
rate research
Read More
In the frames of classical mechanics the generalized Langevin equation is derived for an arbitrary mechanical subsystem coupled to the harmonic bath of a solid. A time-acting temperature operator is introduced for the quantum Klein-Kramers and Smoluchowski equations, accounting for the effect of the quantum thermal bath oscillators. The model of Brownian emitters is theoretically studied and the relevant evolutionary equations for the probability density are derived. The Schrodinger equation is explained via collisions of the target point particles with the quantum force carriers, transmitting the fundamental interactions between the point particles. Thus, electrons and other point particles are no waves and the wavy chapter of quantum mechanics originated for the force carriers. A stochastic Lorentz-Langevin equation is proposed to describe the underlaying Brownian-like motion of the point particles in quantum mechanics. Considering the Brownian dynamics in the frames of the Bohmian mechanics, the density functional Bohm-Langevin equation is proposed, and the relevant Smoluchowski-Bohm equation is derived. A nonlinear master equation is proposed by proper quantization of the classical Klein-Kramers equation. Its equilibrium solution in the exact canonical Gibbs density operator, while the well-known Caldeira-Leggett equation is simply a linearization at high temperature. In the case of a free quantum Brownian particles, a new law for the spreading of the wave packet it discovered, which represents the quantum generalization of the classical Einstein law of Brownian motion. A new projector operator is proposed for the collapse of the wave function of a quantum particle moving in a classical environment. Its application results in dissipative Schrodinger equations, as well as in a new form of dissipative Liouville equation in classical mechanics.
The {it exchange} interaction arising from the particle indistinguishability is of central importance to physics of many-particle quantum systems. Here we study analytically the dynamical generation of quantum entanglement induced by this interaction in an isolated system, namely, an ideal Fermi gas confined in a chaotic cavity, which evolves unitarily from a non-Gaussian pure state. We find that the breakdown of the quantum-classical correspondence of particle motion, via dramatically changing the spatial structure of many-body wavefunction, leads to profound changes of the entanglement structure. Furthermore, for a class of initial states, such change leads to the approach to thermal equilibrium everywhere in the cavity, with the well-known Ehrenfest time in quantum chaos as the thermalization time. Specifically, the quantum expectation values of various correlation functions at different spatial scales are all determined by the Fermi-Dirac distribution. In addition, by using the reduced density matrix (RDM) and the entanglement entropy (EE) as local probes, we find that the gas inside a subsystem is at equilibrium with that outside, and its thermal entropy is the EE, even though the whole system is in a pure state. As a by-product of this work, we provide an analytical solution supporting an important conjecture on thermalization, made and numerically studied by Garrison and Grover in: Phys. Rev. X textbf{8}, 021026 (2018), and strengthen its statement.
The Klein-Kramers equation, governing the Brownian motion of a classical particle in quantum environment under the action of an arbitrary external potential, is derived. Quantum temperature and friction operators are introduced and at large friction the corresponding Smoluchowski equation is obtained. Introducing the Bohm quantum potential, this Smoluchowski equation is extended to describe the Brownian motion of a quantum particle in quantum environment.
Drawing independent samples from a probability distribution is an important computational problem with applications in Monte Carlo algorithms, machine learning, and statistical physics. The problem can in principle be solved on a quantum computer by preparing a quantum state that encodes the entire probability distribution followed by a projective measurement. We investigate the complexity of adiabatically preparing such quantum states for the Gibbs distributions of various classical models including the Ising chain, hard-sphere models on different graphs, and a model encoding the unstructured search problem. By constructing a parent Hamiltonian, whose ground state is the desired quantum state, we relate the asymptotic scaling of the state preparation time to the nature of transitions between distinct quantum phases. These insights enable us to identify adiabatic paths that achieve a quantum speedup over classical Markov chain algorithms. In addition, we show that parent Hamiltonians for the problem of sampling from independent sets on certain graphs can be naturally realized with neutral atoms interacting via highly excited Rydberg states.
The correspondence principle is a cornerstone in the entire construction of quantum mechanics. This principle has been recently challenged by the observation of an early-time exponential increase of the out-of-time-ordered correlator (OTOC) in classically non-chaotic systems [E.B. Rozenbaum et al., Phys. Rev. Lett. 125, 014101 (2020)], Here we show that the correspondence principle is restored after a proper treatment of the singular points. Furthermore our results show that the OTOC maintains its role as a diagnostic of chaotic dynamics.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
