Related papers: Quantum Kinetic Equations and Evolution of Many-Pa…
The rigorous approach to the description of the kinetic evolution of a many-particle system composed of a trace hard sphere and an environment of finitely many hard spheres is developed. We prove that the evolution of states of a trace hard…
A formalism for studying the dynamics of quantum systems embedded in classical spin baths is introduced. The theory is based on generalized antisymmetric brackets and predicts the presence of open-path off-diagonal geometric phases in the…
Understanding and characterising quantum many-body dynamics remains a significant challenge due to both the exponential complexity required to represent quantum many-body Hamiltonians, and the need to accurately track states in time under…
In this Ph.D. thesis dissertation concerns the quantum dynamics of strongly-correlated quantum systems in out-of-equilibrium states. The research is neither restricted to static properties or long-term relaxation evolutions nor does it…
We study the Cauchy problem for an abstract quasilinear stochastic parabolic evolution equation on a Banach space driven by a cylindrical Brownian motion. We prove existence and uniqueness of a local strong solution up to a maximal stopping…
In optimal quantum-mechanical evolutions, motion can take place along paths of minimal length within an optimal time frame. Alternatively, optimal evolutions may occur along established paths without any waste of energy resources and…
A variant of the abstract Cauchy-Kovalevskaya theorem is considered. We prove existence and uniqueness of classical solutions to the nonlinear, non-autonomous initial value problem \[ \frac{du(t)}{dt} = A(t)u(t) + B(u(t),t), \ \ u(0) = x \]…
The quantum many-electron problem is not just at the heart of condensed matter phenomena, but also essential for first-principles simulation of chemical phenomena. Strong correlation in chemical systems are prevalent and present a…
In the present manuscript we consider the Boltzmann equation that models a polyatomic gas by introducing one additional continuous variable, referred to as microscopic internal energy. We establish existence and uniqueness theory in the…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
We investigate the question of unitarity of evolution between hypersurfaces in quantum field theory in curved spacetime from the perspective of the general boundary formulation. Unitarity thus means unitarity of the quantum operator that…
Nonequilibrium states of closed quantum many-body systems defy a thermodynamic description. As a consequence, constraints such as the principle of equal a priori probabilities in the microcanonical ensemble can be relaxed, which can lead to…
The problem of statistics of molecular random walks in a classical fluid is analyzed by means of the BBGKY hierarchy of equations reformulated in terms of the Bogolyubov evolution equation for generating functional of many-particle…
General birth-and-death as well as hopping stochastic dynamics of infinite multicomponent particle systems in the continuum are considered. We derive the corresponding evolution equations for quasi-observables and correlation functions. We…
This monograph addresses an important problem in mathematical fluid dynamics: constructing stable, long-term solutions to certain quasilinear evolution equations. We implement an elaborate scheme for building global quasiperiodic solutions…
Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…
The efficient numerical simulation of nonequilibrium real-time evolution in isolated quantum matter constitutes a key challenge for current computational methods. This holds in particular in the regime of two spatial dimensions, whose…
We present a family of methods, analytical and numerical, which can describe behaviour in (non) equilibrium ensembles, both classical and quantum, especially in the complex systems, where the standard approaches cannot be applied. We…
This article is a brief introduction to quantum algorithms for the eigenvalue problem in quantum many-body systems. Rather than a broad survey of topics, we focus on providing a conceptual understanding of several quantum algorithms that…
We construct a sequence that converges to a solution of the Cauchy problem for a singularly perturbed linear inhomogeneous differential equation of an arbitrary order. This sequence is also an asymptotic sequence in the following sense: the…