Related papers: Gauge fields, point interactions and few-body prob…
The quantum 2-component DS1 system was reduced to two 1D many-body problems with $\delta-$function interactions, which were solved by Bethe ansatz. Using the ansatz in ref.[1] and introducing symmetric and antisymmetric Young operators of…
Boundary conditions may change the phase diagram of non-equilibrium statistical systems like the one-dimensional asymmetric simple exclusion process with and without particle number conservation. Using the quantum Hamiltonian approach, the…
We consider two-point non-self-adjoint boundary eigenvalue problems for linear matrix differential operators. The coefficient matrices in the differential expressions and the matrix boundary conditions are assumed to depend analytically on…
We study a family of differential operators $L_\alpha$ in two variables, depending on the coupling parameter $\alpha\ge0$ that appears only in the boundary conditions. Our main concern is the spectral properties of $L_\alpha$, which turn…
We consider a four-parameter family of point interactions in one dimension. This family is a generalization of the usual $\delta$-function potential. We examine a system consisting of many particles of equal masses that are interacting…
In a trapped Bose-Einstein condensate, subject to the action of an alternating external field, coherent topological modes can be resonantly excited. Depending on the amplitude of the external field and detuning parameter, there are two…
We consider a second order self-adjoint operator in a domain which can be bounded or unbounded. The boundary is partitioned into two parts with Dirichlet boundary condition on one of them, and Neumann condition on the other. We assume that…
Two-level atoms interacting with a one mode cavity field at zero temperature have order parameters which reflect the presence of a quantum phase transition at a critical value of the atom-cavity coupling strength. Two popular examples are…
The phase diagram of the attractive Hubbard model with spatially inhomogeneous interactions is obtained using a single site dynamical mean field theory like approach. The model is characterized by three parameters: the interaction strength,…
As is well-known, there exists a four parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum dependent terms, and we determine…
In this work we define a formal notion of a quantum phase crossover for certain Bethe ansatz solvable models. The approach we adopt exploits an exact mapping of the spectrum of a many-body integrable system, which admits an exact Bethe…
The two parameter model is reduced to a one parameter model by using simple transformations. Because the separation between different phase regions for a one parameter model is just a point, the equivalence between the two models leads to…
We study the phase diagram of the $U(2) \times U(2)$ scalar model in $d=4$ dimensions. We find that the phase transition is of first order in most of the parameter space. The theory can still be relevant to continuum physics (as an…
Nuclear matter at finite temperature and barion density exhibits several phase transitions that could happen at the early stages of the Universe evolution and could be realized in heavy-ion or hadron-hadron collisions. Microscopic…
We study the two dimensional three-body problem in the general case of three distinguishable particles interacting through zero-range potentials. The Faddeev decomposition is used to write the momentum-space wave function. We show that the…
Within the framework of an exactly solvable model, which takes into account the interaction of fluctuating modes with equal and opposite momenta, we consider phase diagrams in systems with coupled scalar order parameters. We show that, in…
We study various dynamical aspects of systems possessing a first order phase transition in their phase diagram. We isolate three qualitatively distinct types of theories depending on the structure of instabilities and the nature of the low…
The dynamics of phase transitions (PT) in quantum field theories at finite temperature is most accurately described within the framework of dimensional reduction. In this framework, thermodynamic quantities are computed within the…
A continuum of excitations in interacting one-dimensional systems is bounded from below by a spectral edge that marks the lowest possible excitation energy for a given momentum. We analyse short-range interactions between Fermi particles…
Coupled phase-oscillators are important models related to synchronization. Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional collective behaviors in coupled oscillator systems. In this paper, we develop a simple…