Related papers: Quantum and classical chaos of a two-electron syst…
The quantum dynamics of a classically chaotic model are studied in the approach to the macroscopic limit. The quantum predictions are compared and contrasted with the classical predictions of both Newtonian and Liouville mechanics. The…
We study the quantum-classical correspondence for systems with interacting spin-particles that are strongly chaotic in the classical limit. This is done in the presence of constants of motion associated with the fixed angular momenta of…
Chaotic quantum systems with Lyapunov exponent $\lambda_\mathrm{L}$ obey an upper bound $\lambda_\mathrm{L}\leq 2\pi k_\mathrm{B}T/\hbar$ at temperature $T$, implying a divergence of the bound in the classical limit $\hbar\to 0$. Following…
The structure of Collapse Models is investigated in the framework of Quantum Measure Theory, a histories-based approach to quantum mechanics. The underlying structure of coupled classical and quantum systems is elucidated in this approach…
We present a complete classification of the electron-electron interaction in chaotic quantum dots based on expansion in inverse powers of $1/M$, the number of the electron states in the Thouless window, $M \simeq k_F R$. This classification…
Quantum chaos is a major subject of interest in condensed matter theory, and has recently motivated new questions in the study of classical chaos. In particular, recent studies have uncovered interesting physics in the relationship between…
The method of restricted path integrals allows one to effectively consider continuous (prolonged in time) measurements of quantum systems. Monitoring of the system coordinates is such a continuous measurement that allows one to describe a…
Classical chaos arises from the inherent non-linearity of dynamical systems. However, quantum maps are linear; therefore, the definition of chaos is not straightforward. To address this, we study a quantum system that exhibits chaotic…
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical…
The Loschmidt echo (LE) is a measure of the sensitivity of quantum mechanics to perturbations in the evolution operator. It is defined as the overlap of two wave functions evolved from the same initial state but with slightly different…
We study the dynamics of a "kicked" quantum system undergoing repeated measurements of momentum. A diffusive behavior is obtained for a large class of Hamiltonians, even when the dynamics of the classical counterpart is not chaotic. These…
We introduce aspects of quantum chaos by analyzing the eigenvalues and the eigenstates of quantum many-body systems. The properties of quantum systems whose classical counterparts are chaotic differ from those whose classical counterparts…
The electrostatic energy of an additional electron on a conducting grain blocks the flow of current through the grain, an effect known as the Coulomb blockade. Current can flow only if two charge states of the grain have the same energy; in…
Most classical dynamical systems are chaotic. The trajectories of two identical systems prepared in infinitesimally different initial conditions diverge exponentially with time. Quantum systems, instead, exhibit quasi-periodicity due to…
We study the level statistics of an interacting multi-qubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasi-energy level statistics show effects analogous to the ones observed in semi-classical…
We investigate the classical motion of three charged particles with both attractive and repulsive interaction.The triple collision is a main source of chaos in such three body Coulomb problems.By employing the McGehee scaling technique, we…
This paper investigates the dynamics of quantum analogs of classical impact oscillators to explore how complex nonlinear behaviors manifest in quantum systems. While classical impact oscillators exhibit chaos and bifurcations, quantum…
We show that the classical dynamics of independent particles can determine the quantum properties of interacting electrons in the ballistic regime. This connection is established using diagrammatic perturbation theory and semiclassical…
The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the…
We use a generalized master equation (GME) formalism to describe the non-equilibrium time-dependent transport of Coulomb interacting electrons through a short quantum wire connected to semi-infinite biased leads. The contact strength…