Related papers: Perturbation theory for confined systems
The elementary excitations of a state of matter consisting of large collection of interacting particles can be very different from the original particles. In the most interesting examples, the particles effectively decompose into smaller…
We develop a perturbation theory of quantum (and classical) master equations with slowly varying parameters, applicable to systems which are externally controlled on a time scale much longer than their characteristic relaxation time. We…
The basic principles of self-organization of one-component charged particles, confined in disk and circular parabolic potentials, are proposed. A system of equations is derived, that allows us to determine equilibrium configurations for an…
We develop a Liouville perturbation theory for weakly driven and weakly open quantum systems in situations when the unperturbed system has a number of conservations laws. If the perturbation violates the conservation laws, it drives the…
The $1s^2->1s2p(^1P)$ excitation in confined and compressed helium atoms in either the bulk material or encapsulated in a bubble is shifted to energies higher than that in the free atom. For bulk helium, the energy shifts predicted from…
We explore the effective long-range interaction of charged particles confined to a curved low-dimensional manifold using the example of a helical geometry. Opposite to the Coulomb interaction in free space the confined particles experience…
We have studied the dynamics and symmetries of a particle constrained to move in a torus knot. The Hamiltonian system turns out to be Second Class in Dirac's formulation and the Dirac brackets yield novel noncommutative structures. The…
We review recent theoretical and experimental advances toward understanding the effects of nuclear spins in confined nanostructures. These systems, which include quantum dots, defect centers, and molecular magnets, are particularly…
Except for the universe, all quantum systems are open, and according to quantum state diffusion theory, many systems localize to wave packets in the neighborhood of phase space points. This is due to decoherence from the interaction with…
For itinerant fermionic and bosonic systems, we study `particle entanglement', defined as the entanglement between two subsets of particles making up the system. We formulate the general structure of particle entanglement in many-fermion…
We study systems of active particles, whose perception is constrained by a vision cone, that are attracted to other particles and repelled from static obstacles. We report a novel self-trapping mechanism: active particles with…
Evidently, some relaxation dynamics, e.g. exponential decays, are much more common in nature than others. Recently there have been attempts to explain this observation on the basis of ``typicality of perturbations'' with respect to their…
We consider the motion of a point particle with spin in a stationary spacetime. We define, following Witzany (2019) and later Ramond (2022), a twelve dimensional Hamiltonian dynamical system whose orbits coincide with the solutions of the…
Packing of particles in confined environments is a common problem in multiple fields. Here, based on the two-dimensional Hertzian particle model, we study the packing of deformable spherical particles under compression, and reveal the…
Using the approach to quantum entanglement based on the quantum fluctuations of observables, we show the existence of perfect entangled states of a single "spin-1" particle. We give physical examples related to the photons, condensed matter…
High temperature expansion of the partition function for a particle on a segment of a line is found to show an example of the quantum system that thermodynamical functions do not approach the thermodynamical functions of its classical…
We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of…
We consider percolation and jamming transitions for particulate systems exposed to compression. For the systems built of particles interacting by purely repulsive forces in addition to friction and viscous damping, it is found that these…
Perturbation theory can be reformulated as dynamical theory. Then a sequence of perturbative approximations is bijective to a trajectory of dynamical system with discrete time, called the approximation cascade. Here we concentrate our…
We consider a classically chaotic system that is described by an Hamiltonian $H(Q,P;x)$ where x is a constant parameter. Our main interest is in the case of a gas-particle inside a cavity, where $x$ controls a deformation of the boundary or…