Related papers: The existence problem for dynamics of dissipative …
We present a semiclassical analysis for a dissipative quantum map with an area-nonpreserving classical limit. We show that in the limit of Planck's constant to 0 the trace of an arbitrary natural power of the propagator is dominated by…
There has been a long-standing and sometimes passionate debate between physicists over whether a dynamical framework for quantum systems should incorporate not completely positive (NCP) maps in addition to completely positive (CP) maps.…
Methods for modeling large driven dissipative quantum systems are becoming increasingly urgent due to recent experimental progress in a number of photonic platforms. We demonstrate the positive-P method to be ideal for this purpose across a…
Models based on non-Hermitian Hamiltonians can exhibit a range of surprising and potentially useful phenomena. Physical realizations typically involve couplings to sources of incoherent gain and loss; this is problematic in quantum…
Linear non-unitary dynamics arise in open quantum systems, non-Hermitian models, and numerical evolution problems, yet current quantum algorithms do not cleanly separate coherent and dissipative effects at the design level. We introduce…
We initiate a study of the following problem: Given a continuous domain $\Omega$ along with its convex hull $\mathcal{K}$, a point $A \in \mathcal{K}$ and a prior measure $\mu$ on $\Omega$, find the probability density over $\Omega$ whose…
For systems described by finite matrices, an affine form is developed for the maps that describe evolution of density matrices for a quantum system that interacts with another. This is established directly from the Heisenberg picture. It…
In the framework of deterministic finslerian models, a mechanism producing dissipative dynamics at the Planck scale is discussed. It is based on a geometric evolution from Finsler to Riemann structures defined on the fiber bundle ${ TM}\to…
A semi-discretization in time, according to a full implicit Euler scheme, for a 2D dissipative quasi geostrophic equation, is studied. We prove existence, uniqueness and regularity results of the solution to the predicted discretization, in…
We discuss dynamical response theory of driven-dissipative quantum systems described by Markovian Master Equations generating semi-groups of maps. In this setting thermal equilibrium states are replaced by non-equilibrium steady states and…
Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian…
Important nonlinear dynamics, such as those found in plasma and fluid systems, are typically hard to simulate on classical computers. Thus, if fault-tolerant quantum computers could efficiently solve such nonlinear problems, it would be a…
Using the known possibility to associate the completely positive maps with density matrices and recent results on expressing the density matrices with sets of classical probability distributions of dichotomic random variables we construct…
We consider a quantum oscillator coupled to a bath of $N$ other oscillators. The total system evolves with a quasi-Hermitian Hamiltonian. Associated to it is a family of Hermitian systems, parameterized by a unitary map $W$. Our main goal…
Considering an $N$-level system interacting factorizably with a continuous spectrum, we derive analytical expressions for the bound states and the dynamical evolution within this single-excitation Friedrichs model by using the projection…
In this paper, we develop a theory of learning nonlinear input-output maps with fading memory by dissipative quantum systems, as a quantum counterpart of the theory of approximating such maps using classical dynamical systems. The theory…
Let $A$ and $(-\widetilde{A})$ be dissipative operators on a Hilbert space $\mathcal{H}$ and let $(A,\widetilde{A})$ form a dual pair, i.e. $A\subset\widetilde{A}^*$, resp.\ $\widetilde{A}\subset A^*$. We present a method of determining the…
We investigate symmetry-resolved entanglement in out-of-equilibrium fermionic systems subject to gain and loss dissipation, which preserves the block-diagonal structure of the reduced density matrix. We derive a hydrodynamic description of…
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…
Exposed positive maps in matrix algebras define a dense subset of extremal maps. We provide a sufficient condition for a positive map to be exposed. This is an analog of a spanning property which guaranties that a positive map is optimal.…