Universal theory of nonlinear Luttinger liquids

One-dimensional quantum fluids are conventionally described by using an effective hydrodynamic approach known as Luttinger liquid theory. As the principal simplification, a generic spectrum of the constituent particles is replaced by a linear one, which leads to a linear hydrodynamic theory. We show that to describe the measurable dynamic response functions one needs to take into account the nonlinearity of the generic spectrum and thus of the resulting quantum hydrodynamic theory. This nonlinearity leads, for example, to a qualitative change in the behavior of the spectral function. The universal theory developed in this article is applicable to a wide class of one-dimensional fermionic, bosonic, and spin systems.Comment: final published version with supporting online materia

Pairing of 1D Bose-Fermi mixtures with unequal masses

We have considered one-dimensional Bose-Fermi mixture with equal densities and unequal masses using numerical density matrix renormalization group (DMRG). For the mass ratio of K-Rb mixture and attraction between bosons and fermions, we determined the phase diagram. For weak boson-boson interactions, there is a direct transition between two-component Luttinger liquid and collapsed phases as the boson-fermion attraction is increased. For strong enough boson-boson interactions, we find an intermediate "paired" phase, which is a single-component Luttinger liquid of composite particles. We investigated correlation functions of such a "paired" phase, studied the stability of "paired" phase to density imbalance, and discussed various experimental techniques which can be used to detect it.Comment: 7 pages, 5 figure

Mapping of Coulomb gases and sine-Gordon models to statistics of random surfaces

We introduce a new class of sine-Gordon models, for which interaction term is present in a region different from the domain over which quadratic part is defined. We develop a novel non-perturbative approach for calculating partition functions of such models, which relies on mapping them to statistical properties of random surfaces. As a specific application of our method, we consider the problem of calculating the amplitude of interference fringes in experiments with two independent low dimensional Bose gases. We calculate full distribution functions of interference amplitude for 1D and 2D gases with nonzero temperatures.Comment: final published versio

The fate of 1D spin-charge separation away from Fermi points

We consider the dynamic response functions of interacting one dimensional spin-1/2 fermions at arbitrary momenta. We build a non-perturbative zero-temperature theory of the threshold singularities using mobile impurity Hamiltonians. The interaction induced low-energy spin-charge separation and power-law threshold singularities survive away from Fermi points. We express the threshold exponents in terms of the spinon spectrum.Comment: 5 pages, 1 figur

A Possibility to Observe Short-Range NN Properties in the Deuteron Breakup pd→ppnpd\to ppn

Quasi-binary reaction of the deuteron breakup $p+d\to (pp)+n$ with the final proton-proton pair $(pp)$ in the $^1S_0$ state is analyzed at initial energies $0.5 - 2$ GeV in the kinematics of backward elastic pd-scattering $pd\to dp$. On the basis of the main mechanisms of the $pd\to dp$ process, including initial and final state interaction, we show that unpolarized cross section and spin observables of this reaction exhibit important properties of the half-off-shell $pp(^1S_0)$-scattering amplitude, which are relevant to the nucleon-nucleon interaction at short distances.Comment: 9 pages, Latex, 3 Postscript figure

On contribution of three-body forces to NdNd interaction at intermediate energies

Available data on large-angle nucleon-deuteron elastic scattering $Nd\to dN$ below the pion threshold give a signal for three-body forces. There is a problem of separation of possible subtle aspects of these forces from off-shell effects in two-nucleon potentials. By considering the main mechanisms of the process, we show qualitatively that in the quasi-binary reaction $N+d\to (NN)+N$ with the final spin singlet NN-pair in the S-state the relative contribution of the 3N forces differs substantially from the elastic channel. It gives a new testing ground for the problem in question.Comment: 9 pages, Latex, 3 Postscript figure

Phenomenology of One-Dimensional Quantum Liquids Beyond the Low-Energy Limit

We consider zero temperature behavior of dynamic response functions of 1D systems near edges of support in momentum-energy plane $(k, \omega).$ The description of the singularities of dynamic response functions near an edge $\epsilon(k)$ is given by the effective Hamiltonian of a mobile impurity moving in a Luttinger liquid. For Galilean-invariant systems, we relate the parameters of such an effective Hamiltonian to the properties of the function $\epsilon (k).$ This allows us to express the exponents which characterize singular response functions of spinless bosonic or fermionic liquids in terms of $\epsilon(k)$ and Luttinger liquid parameters for any $k.$ For an antiferromagnetic Heisenberg spin-1/2 chain in a zero magnetic field, SU(2) invariance fixes the exponents from purely phenomenological considerations.Comment: final published versio