Related papers: On the universal constraints for relaxation rates …
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
The implications of a Generalized Uncertainty Principle on the Taub cosmological model are investigated. The model is studied in the ADM reduction of the dynamics and therefore a time variable is ruled out. Such a variable is quantized in a…
Universal scaling near phase transitions is one of the central ideas of physics, linking the growth of spatial correlations to the slowing down of dynamics. So far, direct experimental access to this critical behavior has remained largely…
We show that the discrete-time evolution of an open quantum system generated by a single quantum channel $T$ can be embedded in the discrete-time evolution of an enlarged closed quantum system, i.e. we construct a unitary dilation of the…
We describe a broad dynamical-algebraic framework for analyzing the quantum control properties of a set of naturally available interactions. General conditions under which universal control is achieved over a set of subspaces/subsystems are…
In this paper we introduce the concept of universal stabilizability: the condition that every solution of a nonlinear system can be globally stabilized. We give sufficient conditions in terms of the existence of a control contraction…
We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant…
A kinetic theory for quantum Langmuir waves interacting nonlinearly with quantum ion-acoustic waves is derived. The formulation allows for a statistical analysis of the quantum correction to the Zakharov system. The influence of a…
Dynamical universality is the observation that the dynamical properties of different systems might exhibit universal behavior that are independent of the system details. In this paper, we study the long-time dynamics of an one-dimensional…
The probabilistic description of finite classical systems often leads to linear kinetic equations. A set of physically motivated mathematical requirements is accordingly formulated. We show that it necessarily implies that solutions of such…
Are Markovian master equations for quantum Brownian motion independent of model assumptions used in the derivation and, thus, universal? With the aim of answering this question, we use a random band-matrix model for the system-bath…
Given a discrete quantum group $H$ with a finite normal quantum subgroup $G$, we show that any positive, possibly unbounded, harmonic function on $H$ with respect to an irreducible invariant random walk is $G$-invariant. This implies that,…
It is shown in the paper that the unitary quantum dynamics in quantum mechanics is the universal quantum driving force to speed up a quantum computation. This assertion supports strongly in theory that the unitary quantum dynamics is the…
Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or `principles') of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation,…
A general approach to obtain reduced models for a wide class of discrete-time quantum systems is proposed. The obtained models not only reproduce exactly the output of a given quantum model, but are also guaranteed to satisfy physical…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
Superconducting qubits are an attractive platform for quantum computing since they have demonstrated high-fidelity quantum gates and extensibility to modest system sizes. Nonetheless, an outstanding challenge is stabilizing their…
We introduce a general formalism, based on the stochastic formulation of quantum mechanics, to obtain localized quasi-classical wave packets as dynamically controlled systems, for arbitrary anharmonic potentials. The control is in general…
The quantum walks in the lattice spaces are represented as unitary evolutions. We find a generator for the evolution and apply it to further understand the walks. We first extend the discrete time quantum walks to continuous time walks.…
We present a procedure for averaging one-parameter random unitary groups and random self-adjoint groups. Central to this is a generalization of the notion of weak convergence of a sequence of measures and the corresponding generalization of…