Related papers: Classical and Quantum Mechanics of Anyons
We consider the quantum-classical correspondence from a classical perspective by discussing the potential for chaotic systems to support behaviors normally associated with quantum mechanical systems. Our main analytical tool is a chaotic…
In classical mechanics, a light particle bound by a strong elastic force just oscillates at high frequency in the region allowed by its initial position and velocity. In quantum mechanics, instead, the ground state of the particle becomes…
We numerically investigate the stability of exceptional periodic classical trajectories in rather generic chaotic many-body systems and explore a possible connection between these trajectories and exceptional nonthermal quantum eigenstates…
Quantum chaos of many-body systems has been swiftly developing into a vibrant research area at the interface between various disciplines, ranging from statistical physics to condensed matter to quantum information and to cosmology. In…
Semiclassical mechanics of systems with first-class constraints is developed. Starting from the quantum theory, one investigates such objects as semiclassical states and observables, semiclassical inner product, semiclassical gauge…
We describe classical orbits and quantum states of a three particle system which is weakly chaotic. The quantum energies of the lowest 48 states which are invariant under permutations are given both in various approximations and to high…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
The understanding of how classical dynamics can emerge in closed quantum systems is a problem of fundamental importance. Remarkably, while classical behavior usually arises from coupling to thermal fluctuations or random spectral noise, it…
We investigate whether quantum theory can be understood as the continuum limit of a mechanical theory, in which there is a huge, but finite, number of classical 'worlds', and quantum effects arise solely from a universal interaction between…
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 quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
We study a quantum oscillator interacting and back-reacting on a classical oscillator. This can be done consistently provided the quantum system decoheres, while the backreaction has a stochastic component which causes the classical system…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
The paper introduces a simple quantum model to calculate in a general way allowed frequencies and energy levels of the anharmonic oscillator. The theoretical basis of the approach has been introduced in two early papers aimed to infer the…
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the possibility of entanglement between two or more…
Classical dynamics is formulated as a Hamiltonian flow on phase space, while quantum mechanics is formulated as a unitary dynamics in Hilbert space. These different formulations have made it difficult to directly compare quantum and…
The semiclassical quantization conditions for all partial waves are derived for bound states of two interacting anyons in the presence of a uniform background magnetic field. Singular Aharonov-Bohm-type interactions between the anyons are…
The collective dynamics of a many-body system is described as a special case of low-energy quantum dynamics, occurring when the ground state breaks a continuous symmetry of the Hamiltonian. This approach is applied to the spontaneous…
We study "the Caged Anisotropic Harmonic Oscillator", which is a new example of a superintegrable, or accidentally degenerate Hamiltonian. The potential is that of the harmonic oscillator with rational frequency ratio (l:m:n), but…
The first-order, infinite-component field equations we proposed before for non-relativistic anyons (identified with particles in the plane with noncommuting coordinates) are generalized to accommodate arbitrary background electromagnetic…