Related papers: Quantum Smoluchowski equation: Escape from a metas…
A quantum spline is a smooth curve parameterised by time in the space of unitary transformations, whose associated orbit on the space of pure states traverses a designated set of quantum states at designated times, such that the trace norm…
In this thesis, we develop analytical methods to study out-of-equilibrium stochastic processes driven by colored noise, i.e., noise with temporal correlations. These non-Markovian processes pose significant analytical challenges compared to…
An alternative equilibrium stochastic dynamics for a Brownian particle in inhomogeneous space is derived. Such a dynamics can model the motion of a complex molecule in its conformation space when in equilibrium with a uniform heat bath. The…
Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schr\"odinger-Langevin or Kostin quantum classical transition wave equation is used and applied resulting in a scaled…
Statistics of molecular random walks in a fluid is considered with the help of Bogolyubov equation for generating functional of distribution functions. An invariance group of this equation is found. It results in many exact relations…
The ground state of Bose-Einstein condensates with attractive particle interaction is metastable. One of the decay mechanisms of the condensate is a collapse by macroscopic quantum tunneling, which can be described by the bounce trajectory…
In this work we develop and apply a path integral formulation for the microscopic degrees of freedom obeying stochastic differential equations to an active Brownian particle (ABP) trapped in a harmonic potential. The formalism allows to…
We investigate a mean-field approach to a quantum brownian particle interacting with a quantum thermal bath at temperature $T$, and subjected to a non-linear potential. An exact, partially classical description of quantum brownian motion is…
We study the small mass limit (or: the Smoluchowski-Kramers limit) of a class of quantum Brownian motions with inhomogeneous damping and diffusion. For Ohmic bath spectral density with a Lorentz-Drude cutoff, we derive the…
In this paper, we propose a novel probabilistic control framework for efficiently controlling an ensemble of quantum systems that can also compensate for the interaction of the systems with the external environment. The main challenge in…
We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce the…
We develop a novel approach aimed at solving the equations of motion of open quantum many-body systems. It is based on a combination of generalized wave function trajectories and matrix product states. We introduce an adaptive quantum…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
This work is devoted to the investigation of the most probable transition time between metastable states for stochastic dynamical systems. Such a system is modeled by a stochastic differential equation with non-vanishing Brownian noise, and…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…
Currents through quantum systems may probe non-analyticities in quantum-critical many-body ground states. For a large class of dissipative quantum critical systems we show that it is possible to obtain the reduced system dynamics in the…
We investigate theoretically the emergence of classical statistical physics in a finite quantum system that is either totally isolated or otherwise subjected to a quantum measurement process. We show via a random matrix theory approach to…
We develop a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby. A stochastic algorithm is constructed to move the walkers up the surface through the…
Quantum Brownian motion in a periodic cosine potential is studied and a simple estimate of the tunneling effect is obtained in the frames of a quasi-equilibrium semiclassical approach. It is shown that the latter is applicable for heavy…
The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…