Related papers: Discrete evolution for the zero-modes of the Quant…
It is shown that, in the infinite size limit, certain systems of globally coupled phase oscillators display low dimensional dynamics. In particular, we derive an explicit finite set of nonlinear ordinary differential equations for the…
We propose to use the effect of measurements instead of their number to study the time evolution of quantum systems under monitoring. This time redefinition acts like a microscope which blows up the inner details of seemingly instantaneous…
In this paper, by analyzing the underlying Lefschetz thimble structure, we study quantum phases in zero-dimensional scalar field theories with complex actions. Using first principles, we derive the Lefschetz thimble equations of these…
The discrete equations of motion for the quantum mappings of KdV type are given in terms of the Sklyanin variables (which are also known as quantum separated variables). Both temporal (discrete-time) evolutions and spatial (along the…
We study the effects of dissipative boundaries in many-body systems at continuous quantum transitions, when the parameters of the Hamiltonian driving the unitary dynamics are close to their critical values. As paradigmatic models, we…
We investigate the application of deformation quantization to the system of a free particle evolving within a universe described by a Friedmann-Lemaitre-Robertson-Walker (FLRW) geometry. This approach allows us to analyze the dynamics of…
It is well-known that the Liouville equation of statistical mechanics is restricted to systems where the total number of particles (N) is fixed. In this paper, we show how the Liouville equation can be extended to systems where the number…
In this paper, We characterize bounded ancient solutions to the time-dependent Stokes system with zero boundary value in various domains, including the half space.
It is shown that the existence of a time operator in the Liouville space representation of both classical and quantum evolution provides a mechanism for effective entropy change of physical states. In particular, an initially effectively…
In this chapter, we intend to explore and review some remarkable dynamical properties of quantum discord under various different open quantum system models. Specifically, our discussion will include several concepts connected to the…
A variety of dynamics in nature and society can be approximately treated as a driven and damped parametric oscillator. An intensive investigation of this time-dependent model from an algebraic point of view provides a consistent method to…
The conditions under which quantum-classical Liouville dynamics may be reduced to a master equation are investigated. Systems that can be partitioned into a quantum-classical subsystem interacting with a classical bath are considered.…
We present a comprehensive study of different phases in the Dicke model incorporating both anisotropy and dissipation. We begin with a concise review of the quantum phase transition in this setting, highlighting how these two parameters…
In the case of a gauge-invariant discrete model of Yang-Mills theory difference self-dual and anti-self-dual equations are constructed.
We study the discrete-time evolution of a transformation on a set of probability measures that is up-dated combining independently the marginals on the atoms of partitions. This model was recently introduced in Baake, Baake and Salamat…
There is a sub-class of the solutions to Quantum Tetrahedron Equation related to the algebraical Pentagon Equation. The Quantum Tetrahedron Equation defines an evolution operator in wholly discrete three dimensional space-time. In this…
Open quantum systems with nearly degenerate energy levels have been shown to exhibit long-lived metastable states in the approach to equilibrium, even when modelled with certain Lindblad-form quantum master equations. This is a result of…
Using finite difference method, time evolution of a typical metal molecule metal system is studied by introducing a new method to solve general related Volterra integro differential equation (IDE). Discretization in time domain is applied…
Derivation-based differential calculi are of great importance in noncommutative geometry, noncommutative gauge theory and integrable systems. In this paper, we propose the connection and curvature from a class of deformed derivation-based…
Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation,…