Related papers: How does geometry affect quantum gases?
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
Various widely-used mean-field type theories for a dilute Bose gas are critically examined in the light of the recent discovery of Bose-Einstein condensation of atomic gases in a confined geometry. By numerically solving the mean-field…
Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics that exploits the differential geometry of the underlying state space. We develop both…
The thermodynamics of ideal gas on the noncommutative geometry in the coherent state formalism is investigated. We first evaluate the statistical interparticle potential and see that there are residual "attraction (repulsion) potential"…
In recent years, ultracold atomic gases confined in curved geometries have attracted considerable theoretical interest. This is motivated by recent realizations of bubble traps in microgravity conditions, which open the possibility of…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
Since electrons in a ballistic regime perceive a carbon nanotube or a graphene layer structure as a continuous medium, we can use the study of the quantum dynamics of one electron constrained to a curve or surface to obtain a qualitative…
An approach is proposed enabling to effectively describe the behaviour of a bosonic system. The approach uses the quantum group $GL_{p,q}(2)$ formalism. In effect, considering a bosonic Hamiltonian in terms of the $GL_{p,q}(2)$ generators,…
The properties of ultracold quantum gases of bosons with dipole-dipole interaction is investigated at finite temperature in the frame of the representative ensembles theory. Self-consistent coupled equations of motion are derived for the…
The physical phase space in gauge systems is studied. Effects caused by a non-Euclidean geometry of the physical phase space in quantum gauge models are described in the operator and path integral formalisms. The projection on the Dirac…
The application of geometry to physics has provided us with new insightful information about many physical theories such as classical mechanics, general relativity, and quantum geometry (quantum gravity). The geometry also plays an…
We theoretically examine equilibrium properties of the harmonically trapped ideal Bose and Fermi gases in the quantum degeneracy regime. We analyze thermodynamic characteristics of gases with a finite number of atoms by means of the known…
We show that quantum dynamics of Bose-Einstein condensates in the weakly interacting regime can be geometrized by a Poincar\'e disk. Each point on such a disk represents a thermofield double state, the overlap between which equals the…
The dynamics of interacting quantum vortices in a quasi-two-dimensional spatially inhomogeneous Bose-Einstein condensate, whose equilibrium density vanishes at two points of the plane with a possible presence of an immobile vortex with a…
Over the last two years, the canonical approach to quantum gravity based on connections and triads has been put on a firm mathematical footing through the development and application of a new functional calculus on the space of gauge…
We consider the grand canonical thermodynamics of a noninteracting scalar field in a static spacetime. We take the nonrelativistic limit of thermodynamic quantities in a way that leaves the curved structure of the background geometry…
The thermodynamic properties of bosons moving in a harmonic trap in an arbitrary number of dimensions are investigated in the grand canonical, canonical and microcanonical ensembles by applying combinatorial techniques developed earlier in…
For the Fermi gas filling the space inside a cubic cavity of a fixed volume, at arbitrary temperatures and number of particles, the thermodynamic characteristics are calculated, namely: entropy, thermodynamic potential, energy, pressure,…