Related papers: Unitary time-evolution in stochastic time-dependen…
In this article we look at stochastic processes with uncertain parameters, and consider different ways in which information is obtained when carrying out observations. For example we focus on the case of a the random evolution of a traded…
Many time-dependent linear partial differential equations of mathematical physics and continuum mechanics can be phrased in the form of an abstract evolutionary system defined on a Hilbert space. In this paper we discuss a general framework…
For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…
The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
Stochastic differential equations in Hilbert space as random nonlinear modified Schroedinger equations have achieved great attention in recent years; of particular interest is the long time behavior of their solutions. In this note we…
We describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be…
A discussion is given of the quantisation of a physical system with finite degrees of freedom subject to a Hamiltonian constraint by treating time as a constrained classical variable interacting with an unconstrained quantum state. This…
An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…
Time evolution of a perturbed thermal state is studied in a quantum-mechanical system with O(N) symmetry. In the limit of large N, time dependence of O(N)-singlet expectation values can be described by classical equations of motion in a…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
Random quantum processes play a central role both in the study of fundamental mixing processes in quantum mechanics related to equilibration, thermalisation and fast scrambling by black holes, as well as in quantum process design and…
Recently, the notion of a quantum acceleration limit has been proposed for any unitary time evolution of quantum systems governed by arbitrary nonstationary Hamiltonians. This limit articulates that the rate of change over time of the…
The discussion is limited to first-class parametrized systems, where the definition of time evolution and observables is not trivial, and to finite dimensional systems in order that technicalities do not obscure the conceptual framework.…
It has been argued that it is incompatible to maintain unitary time-evolution for time-dependent non-Hermitian Hamiltonians when the metric operator is explicitly time-dependent. We demonstrate here that the time-dependent Dyson equation…
Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid…
The sensitivity of the evolution of quantum uncertainties to the choice of the initial conditions is shown via a complex nonlinear Riccati equation leading to a reformulation of quantum dynamics. This sensitivity is demonstrated for systems…
The time-evolution operator corresponding to the fractional-time Schr\"odinger equation is nonunitary because it fails to preserve the norm of the vector state in the course of its evolution. However, in the context of the time-dependent…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…