Related papers: Long time Evolution of Quantum Averages Near Stati…

Precise rules are developed in order to formalize the reasoning processes involved in standard non-relativistic quantum mechanics, with the help of analogies from classical physics. A classical or quantum description of a mechanical system…

We consider curved space quantum corrections to the equations of motion of the inflaton field in the early Universe. Using the stochastic formalism in phase space, we demonstrate that the quantum corrected evolution of the inflaton can…

The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…

We analyze equilibration times of subsystems of a larger system under a random total Hamiltonian, in which the basis of the Hamiltonian is drawn from the Haar measure. We obtain that the time of equilibration is of the order of the inverse…

Without wasting time and effort on philosophical justifications and implications, we write down the conditions for the Hamiltonian of a quantum system for rendering it mathematically equivalent to a deterministic system. These are the…

It is proposed that the event horizon of a black hole is a quantum phase transition of the vacuum of space-time analogous to the liquid-vapor critical point of a bose fluid. The equations of classical general relativity remain valid…

We show that formulating the quantum time of arrival problem in a segment of the real line suggests rephrasing the quantum time of arrival problem to finding states that evolve to unitarily collapse at a given point at a definite time. For…

Precision measurements of frequency are critical to accurate timekeeping, and are fundamentally limited by quantum measurement uncertainties. While for time-independent quantum Hamiltonians, the uncertainty of any parameter scales at best…

Adiabatic limit is the presumption of the adiabatic geometric quantum computation and of the adiabatic quantum algorithm. But in reality, the variation speed of the Hamiltonian is finite. Here we develop a general formulation of adiabatic…

We analyze the response of a complex quantum-mechanical system (e. g., a quantum dot) to a time-dependent perturbation. Assuming the dot energy spectrum and the perturbation to be described by the Gaussian Orthogonal Ensemble of random…

We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian $\mathsf H$ is given, as sum of quadratic forms, by $\mathsf H=…

We study in general the time-evolution of correlation functions in a extended quantum system after the quench of a parameter in the hamiltonian. We show that correlation functions in d dimensions can be extracted using methods of boundary…

We study the quantum evolution under the combined action of the exponentials of two not necessarily commuting operators. We consider the limit in which the two evolutions alternate at infinite frequency. This case appears in a plethora of…

Long-range interacting Hamiltonian systems are believed to relax generically towards non-equilibrium states called "quasi-stationary" because they evolve towards thermodynamic equilibrium very slowly, on a time-scale diverging with particle…

We decompose the quantum adiabatic evolution as the products of gauge invariant unitary operators and obtain the exact nonadiabatic correction in the adiabatic approximation. A necessary and sufficient condition that leads to adiabatic…

After analyzing Dirac's equation, one can suggest that a well-known quantum-mechanical momentum operator is associated with relativistic momentum, rather than with non-relativistic one. Consideration of relativistic energy and momentum…

Using the kinematic constraints of classical bodies we construct the allowable wavefunctions corresponding to classical solids. These are shown to be long lived metastable states that are qualitatively far from eigenstates of the true…

We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…

The speed limit provides an upper bound for the dynamical evolution time of a quantum system. Here, we introduce the notion of quantum acceleration limit for unitary time evolution of quantum systems under time-dependent Hamiltonian. We…

A genuine feature of projective quantum measurements is that they inevitably alter the mean energy of the observed system if the measured quantity does not commute with the Hamiltonian. Compared to the classical case, Jacobs proved that…