Related papers: Lyapunov exponent in quantum mechanics. A phase-sp…
We compute semi-analytic and numerical estimates for the largest Lyapunov exponent in a many-particle system with long-range interactions, extending previous results for the Hamiltonian Mean Field model with a cosine potential. Our results…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
The Lyapunov exponent characterizes the asymptotic behavior of long matrix products. Recognizing scenarios where the Lyapunov exponent is strictly positive is a fundamental challenge that is relevant in many applications. In this work we…
I propose a new and direct connection between classical mechanics and quantum mechanics where I derive the quantum mechanical propagator from a variational principle. This variational principle is Hamilton's modified principle generalized…
A probabilistic interpretation of one-particle relativistic quantum mechanics is proposed. Quantum Action Principle formulated earlier is used for to make the dynamics of the Minkowsky time variable of a particle to be classical. After…
This thesis is concerned with the representation theory of the Heisenberg group and its applications to both classical and quantum mechanics. We continue the development of $p$-mechanics which is a consistent physical theory capable of…
We investigate the transition from quantum to classical mechanics using a one-dimensional free particle model. In the classical analysis, we consider the initial positions and velocities of the particle drawn from Gaussian distributions.…
The Lyapunov exponent is well-known in deterministic dynamical systems as a measure for quantifying chaos and detecting coherent regions in physically evolving systems. In this Letter, we show how the Lyapunov exponent can be unified with…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…
Despite the prominent importance of the Lyapunov exponents for characterizing chaos, it still remains a challenge to measure them for large experimental systems, mainly because of the lack of recurrences in time series analysis. Here we…
We use spin coherent states to compare classical and quantum evolution of a simple paradigmatic, discrete-time quantum dynamical system exhibiting chaotic behavior in the classical limit. The spin coherent states are employed to define a…
We discuss the generalized quantum Lyapunov exponents $L_q$, defined from the growth rate of the powers of the square commutator. They may be related to an appropriately defined thermodynamic limit of the spectrum of the commutator, which…
Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…
Classical quasi-integrable systems are known to have Lyapunov times much shorter than their ergodicity time, but the situation for their quantum counterparts is less well understood. As a first example, we examine the quantum Lyapunov…
It has been established that endowing classical phase space with a Riemannian metric is sufficient for describing quantum mechanics. In this letter we argue that, while sufficient, the above condition is certainly not necessary in passing…
We compute Lyapunov spectra for Coulombic and gravitational versions of the one-dimensional systems of parallel sheets with periodic boundary conditions. Exact time evolution of tangent-space vectors are derived and are utilized toward…
We present a simple way to quantize the well-known Margulis expander map. The result is a quantum expander which acts on discrete Wigner functions in the same way the classical Margulis expander acts on probability distributions. The…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A distinct feature of Hermitian quantum chaotic dynamics is the exponential increase of certain out-of-time-order-correlation (OTOC) functions around the Ehrenfest time with a rate given by a Lyapunov exponent. Physically, the OTOCs…