Related papers: Classical and Quantum Mechanics of Anyons
Anyons are quasiparticles in two-dimensional systems that show statistical properties very distinct from those of bosons or fermions. While their isolated observation has not yet been achieved, here we perform a quantum simulation of anyons…
We study the classical mechanics and dynamics of particles that retains some memory of quantum statistics. Our work builds on earlier work on the statistical mechanics and thermodynamics of such particles. Starting from the effective…
Synthetic anyons can be implemented in a noninteracting many-body system, by using specially tailored localized (physical) probes, which supply the demanded nontrivial topology in the system. We consider the Hamiltonian for noninteracting…
The question of anyon interactions and their possible binding plays a key role in the physics of fractional quantum Hall states. Here, we introduce a controlled and scalable approach to study anyon binding by working entirely within the…
The study of quantum mechanical few-body systems is a century old pursuit relevant to countless subfields of physics. While the two-body problem is generally considered to be well-understood theoretically and numerically, venturing to three…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
Owing to their long-lifetimes at cryogenic temperatures, mechanical oscillators are recognized as an attractive resource for quantum information science and as a testbed for fundamental physics. Key to these applications is the ability to…
The many-anyons wavefunction is constructed via the superposition of all the permutations on the direct product of single anyon states and its interchange properties are examined. The phase of permutation is not a representation but the…
Both the set of quantum states and the set of classical states described by symplectic tomographic probability distributions (tomograms) are studied. It is shown that the sets have common part but there exist tomograms of classical states…
The quantization of many-body systems with balanced loss and gain is investigated. Two types of models characterized by either translational invariance or rotational symmetry under rotation in a pseudo-Euclidean space are considered. A…
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…
The exact equations of motion for microscopic density of classical particles number with account of inter-particle interactions and external field in closed form are derived. An integral equation for equilibrium distributions of the…
Certain aspects of the integrability/solvability of the Calogero-Sutherland-Moser systems and the Ruijsenaars-Schneider-van Diejen systems with rational and trigonometric potentials are reviewed. The equilibrium positions of classical…
The nature of the behaviour of an isolated many-body quantum system periodically driven in time has been an open question since the beginning of quantum mechanics. After an initial transient, such a system is known to synchronize with the…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We study self-oscillations of an optomechanical system, where coherent mechanical oscillations are induced by a driven optical or microwave cavity, for the case of an anharmonic mechanical oscillator potential. A semiclassical analytical…
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…
A non-Abelian theory of fermions interacting with gauge bosons, the constrained system, is studied. The equations of motion for a singular system are obtained as total differential equations in many variables. The integrability conditions…
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…
Given a quantum Hamiltonian, we explain how the dynamical properties of the underlying classical system affect the behaviour of quantum eigenstates in the semi-classical limit. We study this problem via the notion of semiclassical measures.…