Related papers: Comment on ``Exact bosonization for an interacting…
The paper gives a detailed survey of recent results on elliptic problems in Hilbert spaces of generalized smoothness. The latter are the isotropic H\"ormander spaces $H^{s,\varphi}:=B_{2,\mu}$, with $\mu(\xi)=<\xi>^{s}\varphi(<\xi>)$ for…
Point-contact Andreev reflection spectroscopy (PCAR) has proven to be one of the most powerful tools in the investigation of superconductors, where it provides information on the order parameter (OP), a fundamental property of the…
We discuss recent results on bosonization in $d \geq 2$ space-time dimensions by giving a very simple derivation for the bosonic representation of the original free fermionic model both in the abelian and non-abelian cases. We carefully…
We present in detail the bosonization-refermionization solution of the anisotropic version of the two-channel Anderson model at a particular manifold in the space of parameters of the theory, where we establish an equivalence with a…
We show that the DC Josephson effect with ultracold fermionic gases in the BEC regime of composite molecules can be described by a nonlinear Schrodinger equation (NLSE). By comparing our results with Bogoliubov-de Gennes calculations [Phys.…
I present a set of remarks related to joint works \cite{paper1},\cite{paper2},\cite{paper3},\cite{MMNO}. These are remarks about polynomials solutions and vertex operators, eigenproblem for polynomials and a remark related to the the…
The spectral function and dynamic structure factor of bosons interacting by contact repulsion and confined to one dimension exhibit power-law singularities along the dispersion curves of the collective modes. We find the corresponding…
We consider a system of fermions with local interactions on a lattice (Hubbard model) and apply a novel extension of the Laplace's method (saddle-point approximation) for evaluating the corresponding partition function. There, we introduce…
We derive classes of exact solitonic solutions of the time-dependent Gross-Pitaevskii equation with repulsive and attractive interatomic interactions. The solutions correspond to a string of bright solitons with phase difference between…
We approach the issue of exponentiation of soft gauge boson corrections to scattering amplitudes from a path integral point of view. We show that if one represents the amplitude as a first quantized path integral in a mixed…
We consider density-imbalanced Fermi gases of atoms in the strongly interacting, i.e. unitarity, regime. The Bogoliubov-deGennes equations for a trapped superfluid are solved. They take into account the finite size of the system, as well as…
Finding spherically symmetric exact solutions in modified gravity is usually a difficult task. In this paper we use the Noether's symmetry approach for a modified Teleparallel theory of gravity labelled as $f(T,B)$ gravity where $T$ is the…
We develop a new method that allows us to map models of interacting fermions onto bosonic models describing collective excitations in an arbitrary dimension. This mapping becomes exact in the thermodynamic continuous time limit. The boson…
A recently proposed path-integral bosonization scheme for massive fermions in $3$ dimensions is extended by keeping the full momentum-dependence of the one-loop vacuum polarization tensor. This makes it possible to discuss both the massive…
We show that a two-dimensional (2D) spin-polarised Fermi gas immersed in a 3D Bose-Einstein condensate (BEC) constitutes a very promising system to realise a $p_x+ip_y$ superfluid. The fermions attract each other via an induced interaction…
The diffusion quantum Monte Carlo technique is used to solve the many-body Schroedinger equation fully quantum mechanically and nonperturbatively for bosonic atomic gases in cigar-shaped confining potentials. By varying the aspect ratio of…
We discuss typical experimental signatures for the Bose-Einstein condensation (BEC) of an ultracold Bose gas in an inhomogeneous optical lattice at finite temperature. Applying the Hartree-Fock-Bogoliubov-Popov formalism, we calculate…
The dynamics of neutrally buoyant particles transported by a turbulent flow is investigated for spherical particles with radii of the order of the Kolmogorov dissipative scale or larger. The pseudo-penalisation spectral method that has been…
By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter $\xi$…
Recent theoretical and experimental progress on studying one-dimensional systems of bosonic, fermionic, and Bose-Fermi mixtures of a few ultracold atoms confined in traps is reviewed in the broad context of mesoscopic quantum physics. We…