Related papers: Gibbs states, algebraic dynamics and generalized R…
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
Current studies about the continuous-variable systems in non-Hermitian quantum mechanics heavily revolved around the singularities in the eigenspectrum by mimicking their discrete-variable counterparts. Discussions over the nonunitary…
Driven many-body quantum systems where some parameter in the Hamiltonian is varied quasiperiodically in time may exhibit nonequilibrium steady states that are qualitatively different from their periodically driven counterparts. Here we…
The it Global Time Theory (GTT) is the further development of the General Relativity (GR). GTT significantly differs from GR in the general physical concepts, but retains 90% of the mathematical structure and main results. The dynamics…
We show that the phase-space formulation of general probabilistic theories can be extended to include a generalized time-evolution and that it can describe a nonquantum hydrogen-like system which is stable, has discrete energy levels, and…
The dynamical convergence of a system to the thermal distribution, or Gibbs state, is a standard assumption across all of the physical sciences. The Gibbs state is determined just by temperature and the system's energies alone. But at…
The time evolution of the Wigner function for Gaussian states generated by Lindblad quantum dynamics is investigated in the semiclassical limit. A new type of phase-space dynamics is obtained for the centre of a Gaussian Wigner function,…
The quantum description of time evolution in non-linear gravitational systems such as cosmological space-times is not well understood. We show, in the simplified setting of mini-superspace, that time evolution of this system can be obtained…
We pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
The quantum measurement axiom dictates that physical observables and in particular the Hamiltonian must be diagonalizable and have a real spectrum. For a time-independent Hamiltonian (with a discrete spectrum) these conditions ensure the…
We propose a complete treatment of a local in time dynamics of open quantum systems. In this approach Markovian evolution turns out to be a special case of a general non-Markovian one. We provide a general representation of the local…
A novel scheme to simulate the evolution of a restricted set of observables of a quantum system is proposed. The set comprises the spectrum-generating algebra of the Hamiltonian. The idea is to consider a certain open-system evolution,…
A non-Hermitian PT-symmetric version of the kicked top is introduced to study the interplay of quantum chaos with balanced loss and gain. The classical dynamics arising from the quantum dynamics of the angular momentum expectation values…
This work concerns a study of the quantum mechanical extension of the work of Horwitz et al. [1] on the stability of classical Hamiltonian systems by geometrical methods. Simulations are carried out for several important examples, these…
Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the…
Relaxing the postulates of an axiomatic theory is a natural way to find more general theories, and historically, the discovery of non-Euclidean geometry is a famous example of this procedure. Here, we use this way to extend quantum…
A systematic perturbation scheme is developed for approximate solutions to the time-dependent Schroedinger equation with a space-adiabatic Hamiltonian. For a particular isolated energy band, the basic approach is to separate kinematics from…
Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems,…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
We consider quantum (unitary) continuous time evolution of spins on a lattice together with quantum evolution of the lattice itself. In physics such evolution was discussed in connection with quantum gravity. It is also related to what is…