The Bose Gas and Asymmetric Simple Exclusion Process on the Half-Line

In this paper we find explicit formulas for: (1) Green’s function for a system of one-dimensional bosons interacting via a delta-function potential with particles confined to the positive half-line; and (2) the transition probability for the one-dimensional asymmetric simple exclusion process (ASEP) with particles confined to the nonnegative integers. These are both for systems with a finite number of particles. The formulas are analogous to ones obtained earlier for the Bose gas and ASEP on the line and integers, respectively. We use coordinate Bethe Ansatz appropriately modified to account for confinement of the particles to the half-line. As in the earlier work, the proof for the ASEP is less straightforward than for the Bose gas.     

The Fermi gas model of one-dimensional conductors

The Fermi gas model of one-dimensional conductors is reviewed. The exact solutions known for particular values of the coupling constants in a single chain problem (Tomonaga model, Luther-Emery model) are discussed. Renormalization group arguments are used to extend these solutions to arbitrary values of the couplings. The instabilities and possible ground states are studied by investigating the behaviour of the response functions. The relationship between this model and others is discussed and is used to obtain further information about the behaviour of the system. The model is generalized to a set of coupled chains to describe quasi-one-dimensional systems. The crossover from one-dimensional to three-dimensional behaviour and the type of ordering are discussed.     

Proposal of a one-dimensional electron gas in the steps at the LaAlO3-SrTiO3 interface

The two-dimensional electron gas at the interface between LaAlO(3) and SrTiO(3) has become one of the most fascinating and highly debated oxide systems of recent times. Here we propose that a one-dimensional electron gas can be engineered at the step edges of the LaAlO(3)/SrTiO(3) interface. These predictions are supported by first-principles calculations and electrostatic modeling which elucidate the origin of the one-dimensional electron gas as an electronic reconstruction to compensate a net surface charge in the step edge. The results suggest a novel route to increasing the functional density in these electronic interfaces.     

Hartree-Fock approximation for the one-dimensional electron gas

The Hartree-Fock calculation on the one-dimensional electron gas is done on the basis of the method analogous to that applied by Bloch and Wigner and Seitz for the three-dimensional gas. The boundary conditions of the standing wave are taken for the wave function and the bare Coulomb interaction between electrons is assumed. The parameterr _s of the three-dimensional gas is replaced by the ratio between the cross-section radius and the length of the potential tube filled by the one-dimensional gas. Excepting for a special case of the excitement of an electron pair put on one electron level the excitation energies of the non-magnetic gas are found to be very much higher than these of the ferromagnetic gas. A similar relation holds between the ground state energies of the non-magnetic and magnetic gases.     

The lattice gas model of fractional quantum hall effect

The two-dimensional interacting electron gas under a strong homogeneous magnetic field is approximated by the one-dimensional classical lattice gas. We show that in our model the eigenstates of the system approach single-particle Slater determinants in the large particle number limit. Cusps in the energy of our model are found at simple fractional occupations.     

Dynamics of an Ultracold Bose Gas in Funnel-Shaped Potential

In this paper we develop a variational theory to study the dynamicproperties of ultracold Bose gas in a funnel external potential. We obtain one-dimensional nonlinear equation which describes the dynamics of transverse tight confined bosonic gas from three-dimension to one-dimension, and find one-dimensional s-wave scattering length which depends on the shape oftransverse confining potential. If the funnel trapping potential is strong enough at zero temperature, all transverse excitations are frozen. We find the dynamic equation which describes the Tonks-Girardeau gas and present a qualitative analysis of the experimental accessibility of the Tonks-Girardeau gas with funnel-trapped alkalic atoms.     

Current progress on heat conduction in one-dimensional gas channels

We give a brief review of the past development of model studies on one-dimensional heat conduction. Particularly, we describe recent achievements on the study of heat conduction in one-dimensional gas models including the hard-point gas model and billiard gas channel. For a one-dimensional gas of elastically colliding particles of unequal masses, heat conduction is anomalous due to momentum conservation, and the divergence exponent of heat conductivity is estimated as α≈0.33 in k ∼ L ^α . Moreover, in billiard gas models, it is found that exponent instability is not necessary for normal heat conduction. The connection between heat conductivity and diffusion is investigated. Some new progress is reported. A recently proposed model with a quantized degree of freedom to study the heat transport in quasi-one dimensional systems is illustrated in which three distinct temperature regimes of heat conductivity are manifested. The establishment of local thermal equilibrium (LTE) in homogeneous and heterogeneous systems is also discussed. Finally, we give a summary with an outlook for further study about the problem of heat conduction.     

On the Entropy of a One-Dimensional Gas with and without Mixing Using Sinai Billiard

A one-dimensional gas comprising N point particles undergoing elastic collisions within a finite space described by a Sinai billiard generating identical dynamical trajectories are calculated and analyzed with regard to strict extensivity of the entropy definitions of Boltzmann–Gibbs. Due to the collisions, trajectories of gas particles are strongly correlated and exhibit both chaotic and periodic properties. Probability distributions for the position of each particle in the one-dimensional gas can be obtained analytically, elucidating that the entropy in this special case is extensive at any given number N. Furthermore, the entropy obtained can be interpreted as a measure of the extent of interactions between molecules. The results obtained for the non-mixable one-dimensional system are generalized to mixable one- and two-dimensional systems, the latter by a simple example only providing similar findings.     

The Coevolution of Galaxies and Supermassive Black Holes in the Near Universe

A fundamental role is attributed to supermassive black holes (SMBH), and the feedback they generate, in the evolution of galaxies. But theoretical models trying to reproduce the M_SMBH vs. sigma relation (between the SMBH mass and stellar velocity dispersion of the galaxy bulge) make broad assumptions about the physical processes involved. These assumptions are needed due to the scarcity of observational constraints on the relevant physical processes which occur when the SMBH is being fed via mass accretion in active galactic nuclei (AGN). In search for these constraints, our group—AGN integral field spectroscopy (AGNIFS)—has been mapping the gas kinematics as well as the stellar population properties of the inner few hundred parsecs of a sample of nearby AGN hosts. In this contribution, I report on results obtained so far which show gas inflows along nuclear spirals and compact disks in the inner tens to hundreds of pc in nearby AGN hosts which seem to be the sources of fuel to the AGN. As the inflow rates are much larger than the AGN accretion rate, the excess gas must be depleted via formation of new stars in the bulge. Indeed, in many cases, we find ～100 pc circumnuclear rings of recent star formation (ages ～10–500 Myr) that can be interpreted as a signature of coevolution of the host galaxy and its AGN. I also report on the mapping of outflows in ionized gas, which are ubiquitous in Seyfert galaxies, and discuss mass outflow rates and powers.     

Metastable systems driven by colored noise: The stationary state

The influence of the Bardeen-Herring back-jump correlations on the Fermi-Dirac statistics of the one-dimensional nonhomogeneous fermionic lattice gas is studied by the Monte Carlo simulation technique and semianalytically. The resulting distribution is obtained, exhibiting increased population of the lower levels in comparison to the Fermi-Dirac statistics.     

Vibration influence on a region with gas under the adiabatic and isothermal boundary conditions

The influence of vibration on the behavior of the perfect viscous gas inside a rectangular cavity is investigated numerically. The heat and mass transfer processes in gas are compared in the region under the isothermal and adiabatic boundary conditions. The problem is solved in the one-dimensional statement.     

Effect of geometrical constraint on conformational properties of a polymer chain

In this article, we analyse the effect of geometrical constraint on the conformational properties of an infinitely long linear semiflexible polymer chain confined in-between two constraints under good solvent condition in two dimensions. The constraints are two impenetrable stair shaped surface and for two-dimensional space, the surface is a one-dimensional line. The semiflexibility of the chain is accounted by introducing a Boltzmann weight of bending energy required to produce each turn in the chain and good solvent condition was accounted by using self-avoiding walk model of the chain. We have calculated exact critical value of step fugacity required for polymerization of an infinitely long polymer chain confined in-between the constraints for different values of separation between the constraints for directed version of the model. We have also calculated possible maximum, minimum values of the persistent length for such chains and the maximum value of bending energy required for each turn in the chain for few values of separation between the constraints.     

Dynamical transition from a quasi-one-dimensional Bose-Einstein condensate to a Tonks-Girardeau gas

We analyze in detail the expansion of a 1D Bose gas after removing the axial confinement. We show that during its one-dimensional expansion the density of the Bose gas does not follow a self-similar solution. Our analysis is based on a nonlinear Schr?dinger equation with variable nonlinearity whose validity is discussed for the expansion problem, by comparing with an exact Bose-Fermi mapping for the case of an initial Tonks-Girardeau gas. For this case, the gas is shown to expand self-similarly, with a different scaling law compared to the one-dimensional Thomas-Fermi condensate.     

p-Wave interactions in low-dimensional fermionic gases

We study a spin-polarized degenerate Fermi gas interacting via a p-wave Feshbach resonance in an optical lattice. The strong confinement available in this system allows us to realize one- and two-dimensional gases and, therefore, to restrict the asymptotic scattering states of atomic collisions. When aligning the atomic spins along (or perpendicular to) the axis of motion in a one-dimensional gas, scattering into channels with the projection of the angular momentum of /m/ = 1 (or m = 0) can be inhibited. In two and three dimensions, we observe the doublet structure of the p-wave Feshbach resonance. For both the one-dimensional and the two-dimensional gases, we find a shift of the position of the resonance with increasing confinement due to the change in collisional energy. In a three-dimensional optical lattice, the losses on the Feshbach resonance are completely suppressed.     

Ground States of Lattice Gases with “Almost” Convex Repulsive Interactions

To the best of our knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely repulsive and strictly convex interactions. Its ground-state particle configurations do not depend on any other details of the interactions and are known as the generalized Wigner lattices or the most homogeneous particle configurations. The question of the stability of this beautiful and universal result against certain perturbations of the repulsive and convex interactions is interesting in itself. Additional motivations for studying such perturbations come from surface physics (adsorption on crystal surfaces) and theories of correlated fermion systems (recent results on ground-state particle configurations of the one-dimensional spinless Falicov–Kimball model). As a first step, we studied a one-dimensional lattice gas whose two-body interactions are repulsive and strictly convex only from distance 2 on, while its value at distance 1 can be positive or negative, but close to zero. We showed that such a modification makes the ground-state particle configurations sensitive to the tail of the interactions; if the sum of the strengths of the interactions from the distance 3 on is small with respect to the strength of the interaction at distance 2, then particles form two-particle lattice-connected aggregates that are distributed in the most homogeneous way. Consequently, despite breaking of the convexity property, the ground state exhibits the feature known as the complete devil's staircase.     

The Gradient Condition for One-Dimensional Symmetric Exclusion Processes

For every Gibbs measure on the one dimensional lattice Z with translation-invariant potential of finite range, an exchange rate for one-dimensional lattice gas which satisfy both the detailed balance condition relative to the Gibbs measure and the gradient condition is constructed.     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime

Recent experiments on ultracold atomic alkali gases in a one-dimensional optical lattice have demonstrated the transition from a gas of soft-core bosons to a Tonks-Girardeau gas in the hard-core limit, where one-dimensional bosons behave like fermions in many respects. We have studied the underlying many-body physics through numerical simulations which accommodate both the soft-core and hard-core limits in one single framework. We find that the Tonks-Girardeau gas is reached only at the strongest optical lattice potentials. Results for slightly higher densities, where the gas develops a Mott-like phase already at weaker optical lattice potentials, show that these Mott-like short-range correlations do not enhance the convergence to the hard-core limit.     

Membrane gas diffusion measurements with MRI

Gas transport across polymeric membranes is fundamental to many filtering and separation technologies. To elucidate transport mechanisms, and understand the behaviors of membrane materials, accurate measurement of transport properties is required. We report a new magnetic resonance imaging (MRI) methodology to measure membrane gas phase diffusion coefficients. The MRI challenges of low spin density and short gas phase relaxation times, especially for hydrogen gas, have been successfully overcome with a modified one-dimensional, single-point ramped imaging with T(1) enhancement, measurement. We have measured the diffusion coefficients of both hydrogen gas and sulfur-hexafluoride in a model polymeric membrane of potential interest as a gas separator in metal hydride batteries. The experimental apparatus is a modified one-dimensional diaphragm cell which permits measurement of the diffusion coefficient in experimental times of less than 1 min. The H(2) gas diffusion coefficient in the membrane was 0.54 +/- 0.01 mm(2)/s, while that of sulfur-hexafluoride was 0.14 +/- 0.01 mm(2)/s, at ambient conditions.     

Anyon-fermion mapping and applications to ultracold gases in tight waveguides

The Fermi-Bose mapping method for one-dimensional Bose and Fermi gases with zero-range interactions is generalized to an anyon-fermion mapping and applied to exact solution of several models of ultracold gases with anyonic exchange symmetry in tight waveguides: anyonic Calogero-Sutherland model, anyons with point hard-core interaction (anyonic Tonks-Girardeau gas), and spin-aligned anyon gas with infinite zero-range odd-wave attractions (attractive anyonic Tonks-Girardeau, or AATG, gas). It is proved that for even N>or=4 there are states of the AATG gas on a ring, with anyonic phase slips which are odd integral multiples of pi/(N-1), of energy lower than that of the corresponding fermionic ground state. A generalization to a spinor Fermi gas state with anyonic symmetry under purely spatial exchange enables energy lowering by the same mechanism.