Related papers: On the time evolution of fermionic occupation numb…
We consider a one dimensional evolution problem modeling the dynamics of an acoustic field coupled with a set of mechanical oscillators. We analyze solutions of the system of ordinary and partial differential equations with time-dependent…
The evolution equations of quantum observables are derived from the classical Hamiltonian equations of motion with the only additional assumption that the phase space is non-commutative. The demonstration of the quantum evolution laws is…
We use the equations of motion in combination with crossing symmetry to constrain the properties of interacting fermionic boundary conformal field theories. This combination is an efficient way of determining operator product expansion…
One of the axioms of quantum field theory is the property of unitarity of the evolution operator. However, if one considers the quantum electrodynamics in the external field in the leading order of perturbation theory, one will find that…
A novel expansion of the evolution operator associated with a -- in general, time-dependent -- perturbed quantum Hamiltonian is presented. It is shown that it has a wide range of possible realizations that can be fitted according to…
We present random quantum circuit models for non-unitary quantum dynamics of free fermions in one spatial dimension. Numerical simulations reveal that the dynamics tends towards steady states with logarithmic violations of the entanglement…
The mean field limit for systems of many fermions is naturally coupled with a semiclassical limit. This makes the analysis of the mean field regime much more involved, compared with bosonic systems. In this paper, we study the dynamics of…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
The geometric phase is a fundamental quantity characterizing the holonomic feature of quantum systems. It is well known that the evolution operator of a quantum system undergoing a cyclic evolution can be simply written as the product of…
We show that the kinetic approach to statistical mechanics permits an elegant and efficient treatment of fractional exclusion statistics. By using the exclusion-inclusion principle recently proposed [Phys. Rev. E49, 5103 (1994)] as a…
Evolution equations describe the effect of consecutively integrating out all quantum fluctuations with momenta larger than some infrared cutoff scale k. We develop a formalism for the introduction of collective degrees of freedom at some…
The best known manifestation of the Fermi-Dirac statistics is the Pauli exclusion principle: no two identical fermions can occupy the same one-particle state. This principle enforces high order correlations in systems of many identical…
We examine the logical structure of the emergence of classical stochasticity for a quantum system governed by a Pauli-type master equation. It is well-known that while such equations describe the evolution of probabilities, they do not…
Statistical properties of Fermionic Molecular Dynamics are studied. It is shown that, although the centroids of the single--particle wave--packets follow classical trajectories in the case of a harmonic oscillator potential, the equilibrium…
Steady-state observables, such as occupation numbers and currents, are crucial experimental signatures in open quantum systems. The time-convolutionless (TCL) master equation, which is both exact and time-local, is an ideal candidate for…
We consider second-order evolution equations in an abstract setting with intermittently delayed/ not-delayed damping. We give sufficient conditions for asymptotic and exponential stability, improving and generalising our previous results…
The time-evolution operator obtained from the fractional-time Schr\"{o}dinger equation (FTSE) is said to be non-unitary since it does not preserve the norm of the vector state in time. As done in the time-dependent non-Hermitian quantum…
We study the time evolution of two coupled quantum harmonic oscillators interacting through nonlinear optomechanical-like Hamiltonians that include cross-Kerr interactions. We employ techniques developed to decouple the time-evolution…
This article deals with the study of electromagnetic waves equations and the Lorentz condition, as emergent properties of Maxwell's system in the context of systems theory. To do this, the wave equations and the Helmholtz equation are first…
A Dirac picture perturbation theory is developed for the time evolution operator in classical dynamics in the spirit of the Schwinger-Feynman-Dyson perturbation expansion and detailed rules are derived for computations. Complexification…