scholarly journals Quantum quench dynamics of the attractive one-dimensional Bose gas via the coordinate Bethe ansatz

2018 ◽  
Vol 4 (2) ◽  
Author(s):  
Jan Zill ◽  
Tod Wright ◽  
Karen Kheruntsyan ◽  
Thomas Gasenzer ◽  
Matthew Davis
Keyword(s):  
Bethe Ansatz ◽  
Correlation Functions ◽  
Bound States ◽  
Delta Function ◽  
Ideal Gas ◽  
Relaxation Dynamics ◽  
Temperature Correlation ◽  
One Dimensional ◽  
Quench Dynamics

We use the coordinate Bethe ansatz to study the Lieb–Liniger model of a one-dimensional gas of bosons on a finite-sized ring interacting via an attractive delta-function potential. We calculate zero-temperature correlation functions for seven particles in the vicinity of the crossover to a localized solitonic state and study the dynamics of a system of four particles quenched to attractive interactions from the ideal-gas ground state. We determine the time evolution of correlation functions, as well as their temporal averages, and discuss the role of bound states in shaping the postquench correlations and relaxation dynamics.

STRINGS COMPLETE THE SPECTRUM OF 1-D δ-FUNCTION FERMIONS

1993 ◽  
Vol 07 (10) ◽  
pp. 689-698 ◽  
Author(s):  
ERIC D. WILLIAMS
Keyword(s):  
Bethe Ansatz ◽  
Bound States ◽  
Delta Function ◽  
One Dimensional ◽  
Nested Bethe Ansatz ◽  
Function Potential

We study the completeness of the nested Bethe ansatz eigenfunctions for a one dimensional gas of spin-1/2 fermions interacting via a repulsive delta-function potential. We show the completeness of the eigenfunctions for a system in an infinite box with N fermions and the orientation of either one or two of the spins differing from the rest. This demonstrates that the spin bound states (also called Λ-strings) are necessary for completeness of the spectrum.

PHASE SEPARATION AND FFLO PHASES IN ULTRACOLD GAS OF S = 5/2 ATOMS WITH ATTRACTIVE POTENTIAL IN A ONE-DIMENSIONAL TRAP

2012 ◽  
Vol 26 (16) ◽  
pp. 1230009 ◽  
Author(s):  
P. SCHLOTTMANN ◽  
A. A. ZVYAGIN
Keyword(s):  
Phase Separation ◽  
Bethe Ansatz ◽  
Bound States ◽  
Local Density ◽  
Attractive Potential ◽  
Fflo State ◽  
Effective Spin ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
The Rich

In the context of ultracold atoms with effective spin S = 5/2 confined to an elongated trap we study the one-dimensional Fermi gas interacting via an attractive δ-function potential using the Bethe ansatz solution. There are N = 2S + 1 = 6 fundamental states: The particles can either be unpaired or clustered in bound states of 2, 3, …, 2S and 2S + 1 fermions. The rich ground state phase diagram consists of these six states and various mixed phases in which combinations of the fundamental states coexist. Possible scenarios for phase separation due to the harmonic confinement along the tube are explored within the local density approximation. In an array of tubes with weak Josephson tunneling superfluid order may arise. The response functions determining the type of superfluid order are calculated using conformal field theory and the exact Bethe ansatz solution. They consist of a power law with distance times a sinusoidal term oscillating with distance. The wavelength of the oscillations is related to the periodicity of a generalized Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state.

scholarly journals Pascal conductance series in ballistic one-dimensional LaAlO3/SrTiO3 channels

Science ◽  
2020 ◽  
Vol 367 (6479) ◽  
pp. 769-772 ◽  
Author(s):  
Megan Briggeman ◽  
Michelle Tomczyk ◽  
Binbin Tian ◽  
Hyungwoo Lee ◽  
Jung-Woo Lee ◽  
...  
Keyword(s):  
Bound States ◽  
Electronic Systems ◽  
Experimental Setup ◽  
Planck Constant ◽  
Characteristic Sequence ◽  
One Dimensional ◽  
Lanthanum Aluminate ◽  
Quantum Liquids ◽  
Wide Range

One-dimensional electronic systems can support exotic collective phases because of the enhanced role of electron correlations. We describe the experimental observation of a series of quantized conductance steps within strongly interacting electron waveguides formed at the lanthanum aluminate–strontium titanate (LaAlO3/SrTiO3) interface. The waveguide conductance follows a characteristic sequence within Pascal’s triangle: (1, 3, 6, 10, 15, …) ⋅ e2/h, where e is the electron charge and h is the Planck constant. This behavior is consistent with the existence of a family of degenerate quantum liquids formed from bound states of n = 2, 3, 4, … electrons. Our experimental setup could provide a setting for solid-state analogs of a wide range of composite fermionic phases.

INTRINSIC RESONANT TUNNELING PROPERTIES OF THE ONE-DIMENSIONAL SCHRÖDINGER OPERATOR WITH A DELTA DERIVATIVE POTENTIAL

2013 ◽  
Vol 28 (01) ◽  
pp. 1350203 ◽  
Author(s):  
A. V. ZOLOTARYUK ◽  
Y. ZOLOTARYUK
Keyword(s):  
Schrödinger Operator ◽  
Resonant Tunneling ◽  
Bound States ◽  
Delta Function ◽  
Schrodinger Operator ◽  
Range Limit ◽  
One Dimensional ◽  
The One ◽  
Adjoint Operators ◽  
Delta Derivative

Restricting ourselves to a simple rectangular approximation but using properly a two-scale regularization procedure, additional resonant tunneling properties of the one-dimensional Schrödinger operator with a delta derivative potential are established, which appear to be lost in the zero-range limit. These "intrinsic" properties are complementary to the main already proved result that different regularizations of Dirac's delta function produce different limiting self-adjoint operators. In particular, for a given regularizing sequence, a one-parameter family of connection condition matrices describing bound states is constructed. It is proposed to consider the convergence of transfer matrices when the potential strength constant is involved into the regularization process, resulting in an extension of resonance sets for the transmission across a δ′-barrier.

scholarly journals Finite Temperature Correlation Functions of One-dimensional Interacting Electron Systems

2000 ◽  
Vol 53 (4) ◽  
pp. 553 ◽  
Author(s):  
G. Bowen ◽  
M. Gulácsi ◽  
A. Rosengren
Keyword(s):  
Graduate Students ◽  
Correlation Functions ◽  
Finite Temperature ◽  
Electron Systems ◽  
Dimensional Electron ◽  
Temperature Correlation ◽  
One Dimensional

The well-known bosonisation method of one-dimensional electron systems is extended to finite temperatures. As an example, the correlation functions of the non-interacting case are explicitly calculated. The presentation is pedagogical and is intended to be accessible to graduate students or physicists who are not experts in this field.

scholarly journals EXACT RESULTS FOR THE ONE-DIMENSIONAL MANY-BODY PROBLEM WITH CONTACT INTERACTION: INCLUDING A TUNABLE IMPURITY

2007 ◽  
Vol 19 (04) ◽  
pp. 349-370 ◽  
Author(s):  
V. CAUDRELIER ◽  
N. CRAMPÉ
Keyword(s):  
Bethe Ansatz ◽  
Contact Interaction ◽  
Bound States ◽  
Condensed Matter ◽  
Many Body ◽  
One Dimensional ◽  
Special Cases ◽  
Exactly Solvable ◽  
Bethe Equations ◽  
The One

The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

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