Related papers: Stochastic wave function method for non-Markovian …
The dynamical behavior of open quantum systems plays a key role in many applications of quantum mechanics, examples ranging from fundamental problems, such as the environment-induced decay of quantum coherence and relaxation in many-body…
We introduce a transformation of the quantum phase $S'=S+\frac{\hbar}{2}\log\rho$, which converts the deterministic equations of quantum mechanics into the Lagrangian reference frame of stochastic particles. We show that the quantum…
The exact dynamics of a system coupled to an environment can be described by an integro-differential stochastic equation of its reduced density. The influence of the environment is incorporated through a mean-field which is both stochastic…
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…
We consider the problem of minimizing a continuous function given quantum access to a stochastic gradient oracle. We provide two new methods for the special case of minimizing a Lipschitz convex function. Each method obtains a dimension…
We define non-Markovian quantum dynamics as evolution in which the current state depends on all past states, and completely characterize its structure under the assumptions of complete positivity and non-signalling. The resulting…
The theoretical description of quantum dynamics in an intriguing way does not necessarily imply the underlying dynamics is indeed intriguing. Here we show how a known very interesting master equation with an always negative decay rate…
We develop a statistical description of chaotic wavefunctions in closed systems obeying arbitrary boundary conditions by combining a semiclassical expression for the spatial two-point correlation function with a treatment of eigenfunctions…
By modeling the interaction of a system with an environment through a renewal approach, we demonstrate that completely positive non-Markovian dynamics may develop some unexplored non-standard statistical properties. The renewal approach is…
The two-dimensional Hubbard model is studied using the variational quantum Monte Carlo technique with Gutzwiller-type variational wave functions. In addition to the simple one-site correlated Gutzwiller wave function, we use a form with…
We introduce a new method to accurately and efficiently estimate the effective dynamics of collective variables in molecular simulations. Such reduced dynamics play an essential role in the study of a broad class of processes, ranging from…
By means of quantum stochastic calculus we construct a model for an atom with two degenerate levels and stimulated by a laser and we compute its fluorescence spectrum; let us stress that, once the model for the unitary atom-field dynamics…
We theoretically study the non-Markovian dynamics of qubit systems coupled to nonequilibrium environments with nonstationary and non-Markovian statistical properties. The reduced density matrix of the single qubit system satisfies a closed…
Within the f-deformed oscillator formalism, we derive a Markovian master equation for the description of the damped dynamics of nonlinear systems that interact with their environment. The applicability of this treatment to the particular…
We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states. Traditional quantum…
It has been found that Markovian quantum dissipative processes, described by the Lindblad equation, may have attractive steady-state manifolds, in which dissipation and decoherence can play a positive role to quantum information processing.…
Recently, an effective Lindblad master equation for quantum systems whose dynamics are coupled to dissipative bosonic modes has been introduced [Phys. Rev. Lett. 129, 063601 (2022)]. In this approach, the bosonic modes are adiabatically…
We propose an extension of the Schr\"odinger equation for a quantum system interacting with environment. This equation describes dynamics of auxiliary wave-functions $\mathbf{m}$, from which the system density matrix can be reconstructed as…
The act of measurement on a quantum state is supposed to "collapse" the state into one of several eigenstates of the operator corresponding to the observable being measured. This measurement process is sometimes described as outside…
A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum…