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We examine the dynamic and geometric phases of the electron in quantum mechanics using Hestenes' spacetime algebra formalism. First the standard dynamic phase formula is translated into the spacetime algebra. We then define new formulas for…
We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…
We develop a generic method to compute the dynamics induced by quenches in completely connected quantum systems. These models are expected to provide a mean-field description at least of the short time dynamics of finite dimensional system.…
The analysis of a timeseries can provide many new perspectives if it is accompanied by the assumption that the timeseries is generated from an underlying dynamical system. For example, statistical properties of the data can be related to…
We study a two-dimensional fermionic QFT used to model 1D strongly correlated electrons in the presence of a time-dependent impurity that drives the system out of equilibrium. In contrast to previous investigations, we consider a dynamic…
The effect of interactions on dynamics of coupled motor proteins is investigated theoretically. A simple stochastic discrete model, that allows to calculate explicitly the dynamic properties of the system, is developed. It is shown that…
We present a hierarchical equations of motion approach, which allows a numerically exact simulation of nonequilibrium transport in general open quantum systems involving multiple macroscopic bosonic and fermionic environments. The…
We present generic conditions for phase band crossings for a class of periodically driven integrable systems represented by free fermionic models subjected to arbitrary periodic drive protocols characterized by a frequency $\omega_D$. These…
Describing systems with non-Hermitian (NH) operators remains a challenge in quantum theory due to instabilities (e.g., exceptional points and decoherence) arising from interactions with the environment. We propose a framework to express the…
We develop a theoretical description of non-Hermitian time evolution that accounts for the break- down of the adiabatic theorem. We obtain closed-form expressions for the time-dependent state amplitudes, involving the complex eigen-energies…
Periodically driven dynamics of open quantum systems is very interesting because typically non-equilibrium steady state is reached, which is characterized by a non-vanishing current. In this work, we study time discrete and periodically…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
The exact fermion master equation previously obtained in [Phys. Rev. B \textbf{78}, 235311 (2008); New J. Phys. \textbf{12}, 083013 (2010)] describes the dynamics of quantum states of a principal system of fermionic particles under the…
Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally…
Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We experimentally study a periodically driven many-body localized system realized by interacting fermions in a one-dimensional quasi-disordered optical lattice. By preparing the system in a far-from-equilibrium state and monitoring the…
The phase shift rules enable the estimation of the derivative of a quantum state with respect to phase parameters, providing valuable insights into the behavior and dynamics of quantum systems. This capability is essential in quantum…