Related papers: Divisibility of quantum dynamical maps and collisi…
Consider a graph having quantum systems lying at each node. Suppose that the whole thing evolves in discrete time steps, according to a global, unitary causal operator. By causal we mean that information can only propagate at a bounded…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
A new class of critical points, termed as perpetual points, where acceleration becomes zero but the velocity remains non-zero, are observed in dynamical systems. The velocity at these points is either maximum or minimum or of inflection…
We use computer simulations to test a simple idea for mapping between long-time self diffusivities obtained from molecular and Brownian dynamics. The strategy we explore is motivated by the behavior of fluids comprising particles that…
Understanding and simulating how a quantum system interacts and exchanges information or energy with its surroundings is a ubiquitous problem, one which must be carefully addressed in order to establish a coherent framework to describe the…
Two kinds of maps that describe evolution of states of a subsystem coming from dynamics described by a unitary operator for a larger system, maps defined for fixed mean values and maps defined for fixed correlations, are found to be quite…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
For two positive maps $\phi_i:B(\mathcal{K}_i)\to B(\mathcal{H}_i)$, $i=1,2$, we construct a new linear map $\phi:B(\mathcal{H})\to B(\mathcal{K})$, where $\mathcal{K}=\mathcal{K}_1\oplus\mathcal{K}_2\oplus\mathbb{C}$,…
The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…
Phase covariant qubit dynamics describes an evolution of a two-level system under simultaneous action of pure dephasing, energy dissipation, and energy gain with time-dependent rates $\gamma_z(t)$, $\gamma_-(t)$, and $\gamma_+(t)$,…
We investigate the emergence of non-Markovian dynamics in finite-dimensional open quantum systems governed by Weyl dynamical maps and their convex combinations. Using the Hermite normal form, we provide a complete classification of the…
We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…
A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition. The method of the construction applies to more general maps which need…
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…
A remarkable feature of quantum theory is non-locality (i.e. the presence of correlations which violate Bell inequalities). However, quantum correlations are not maximally non-local, and it is natural to ask whether there are compelling…
Starting form a microscopic system-environment model, we construct a quantum dynamical semigroup for the reduced evolution of the open system. The difference between the true system dynamics and its approximation by the semigroup has the…
We extend the usual process-theoretic view on locality and causality in subsystems (based on the tensor product case) to general quantum systems (i.e.\ possibly non-factor, finite-dimensional von Neumann algebras). To do so, we introduce a…
On the example of a quantum oscillator the connection of the dynamical coherent state with the phase symmetry breaking and the existence of the nondissipative motion is considered. In multiparticle systems of interacting particles similar…
Quantum tunneling in a two-dimensional integrable map is studied. The orbits of the map are all confined to the curves specified by the one-dimensional Hamiltonian. It is found that the behavior of tunneling splitting for the integrable map…
Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform directed motion. Extending the paradigm of active matter to a quantum framework…