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By solving the two variable differential equations which arise from finding the eigenfunctions for the Casimir operator for $O(d,2)$ succinct expressions are found for the functions, conformal partial waves, representing the contribution of…
We calculate the energy and condensate fraction for a dense system of bosons interacting through an attractive short range interaction with positive s-wave scattering length $a$. At high densities, $n>>a^{-3}$, the energy per particle,…
We study bosonic atoms in small optical lattices by exact diagonalization and observe a striking similarity to the superfluid to Mott insulator transition in macroscopic systems. The momentum distribution, the formation of an energy gap,…
We study conformal quantum mechanics by first considering the perturbative $S$-matrix in various dimensions. The model has two couplings and we study perturbatively the degree of ultraviolet divergences arising in the interplay between the…
We consider a system of N non-relativistic spinless quantum particles (``electrons'') interacting with a quantized scalar Bose field (whose excitations we call ``photons''). We examine the case when the velocity v of the electrons is small…
Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system.…
The wave function of a dilute hard sphere Bose gas at low temperatures is discussed, emphasizing the formation of pairs. The pair distribution function is calculated for two values of $\sqrt{\rho a^3}$.
Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…
In this article a novel characterization of Bose-Einstein condensates is proposed. Instead of relying on occupation numbers of a few dominant modes, which become macroscopic in the limit of infinite particle numbers, it focuses on the…
A quantum field-theoretical model, which describes spatially non-homogeneous repulsive Bose gas in an external harmonic potential is considered. Two-point thermal correlation functions of the Bose gas are calculated in the framework of the…
The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
We consider dynamic, i.e., frequency-dependent, correlations in non-condensed ultracold atomic Bose gases. In particular, we consider the single-particle correlation function and its power spectrum. We compute this power spectrum for a…
The one-loop partition function for a charged self-interacting Bose gas at finite temperature in D-dimensional spacetime is evaluated within a path integral approach making use of zeta-function regularization. For D even, a new additional…
This work extends the seminal work of Gottfried on the two-body quantum physics of particles interacting through a delta-shell potential to many-body physics by studying a system of non-relativistic particles when the thermal De-Broglie…
The quasiparticle wavefunction of a many-electron system is traditionally defined as the eigenfunction of the quasiparticle eigenvalue equation involving the self-energy. In this article a new concept of a quasiparticle wavefunction is…
For studying the dynamics of a two-level system coupled to a quantum oscillator we have presented an analytical approach, the transformed rotating-wave approximation, which takes into account the effect of the counter-rotating terms but…
Master equations describe the quantum dynamics of open systems interacting with an environment. They play an increasingly important role in understanding the emergence of semiclassical behavior and the generation of entropy, both being…
Here the probability density of relativistic particles coordinates, satisfying the formal conditions of the quantum mechanics and the special relativity, is determined (under textbooks view, such density does not exist). It is specified for…
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…