Related papers: On the universal relations for the formfactors in …
We investigate the response of a one-dimensional Bose gas to a slow increase of its interaction strength. We focus on the rich dynamics of equal-time single-particle correlations treating the Lieb-Liniger model within a bosonization…
We present an exact calculation of the Luttinger liquid relation for the one-dimensional, two-component SC model in the interaction strength range $-1<s<0$ by appropriately varying the limits of the integral Bethe Ansatz equations. The…
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus…
We systematically study ground state properties of fermionic dipolar gases in a planar array of one-dimensional potential tubes for an arbitrary orientation of dipole moments. Using the Luttinger liquid theory with the generalized…
Form factors are calculated in the point form of relativistic quantum mechanics for the lowest energy states of a system made of two scalar particles interacting via the exchange of a massless boson. They are compared to the exact results…
This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…
Exactly solved models provide rigorous understanding of many-body phenomena in strongly correlated systems. In this article, we report a breakthrough in uncovering universal many-body correlated properties of quantum integrable Lieb-Liniger…
Different relativistic quantum mechanics approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current…
The differential cross section for resonant Raman scattering from the collective modes in a one dimensional system of interacting electrons is calculated non-perturbatively using the bosonization method. The results indicate that resonant…
Parametric models in vector spaces are shown to possess an associated linear map. This linear operator leads directly to reproducing kernel Hilbert spaces and affine- / linear- representations in terms of tensor products. From the…
The thermal fluctations of vortices in a superconductor can be usefully mapped onto the quantum fluctations of a collection of bosons at T=0 moving in 2 dimensions. When the superconductor is a thin platelet with the magnetic field parallel…
This series of papers is devoted to identifying and explaining the properties of strongly correlating liquids, i.e., liquids with more than 90% correlation between their virial W and potential energy U fluctuations in the NVT ensemble.…
We use quantum sine-Gordon model to describe the low energy dynamics of a pair of coupled one-dimensional condensates of interacting atoms. We show that the nontrivial excitation spectrum of the quantum sine-Gordon model, which includes…
We study weakly interacting mixtures of ultracold atoms composed of bosonic and fermionic species in 2D and 1D. When interactions between particles are appropriately tuned, self-bound quantum liquids can be formed. We show that while…
We propose a scheme to observe typical strongly correlated fermionic phenomena with bosonic atoms in optical lattices. For different values of the sign and strength of the scattering lengths it is possible to reach a "superconducting"…
The dynamical correlated properties of one-dimensional (1D) Bose gases provide profound understanding of novel physics emergent from collective excitations, for instance, the breakdown of off-diagonal long-range order, and the establishment…
Correlators of large-scale fluctuations produced during cosmic inflation are major observables of inflationary cosmology. In cosmological collider physics, many interesting correlators are generated through loop processes. However,…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
This is an expanded version of a lecture given at the {\it Workshop on Theoretical Methods for Strongly Correlated Fermions}, held at the {\it Centre de Recherches Math\'ematiques}, in Montr\'eal, from May 26 to May 30, 1999. After general…
Many quantum field theories in one, two and four dimensions possess remarkable limits in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the…