Ground state of one-dimension repulsing particles on disordered lattice

2014 ◽  
Vol 25 (08) ◽  
pp. 1450028 ◽  
Author(s):  
L. A. Pastur ◽  
V. V. Slavin ◽  
A. A. Krivchikov
Keyword(s):  
Ground State ◽  
Domain Walls ◽  
Host Lattice ◽  
One Dimension ◽  
Weak Disorder ◽  
Interacting Particles ◽  
One Dimensional ◽  
Lattice Disorder ◽  
Disordered Lattice ◽  
The Mean

The ground state (GS) of interacting particles on a disordered one-dimensional (1D) host-lattice is studied by a new numerical method. It is shown that if the concentration of particles is small, then even a weak disorder of the host-lattice breaks the long-range order of Generalized Wigner Crystal (GWC), replacing it by the sequence of blocks (domains) of particles with random lengths. The mean domains length as a function of the host-lattice disorder parameter is also found. It is shown that the domain structure can be detected by a weak random field, whose form is similar to that of the ground state but has fluctuating domain walls positions. This is because the generalized magnetization corresponding to the field has a sufficiently sharp peak as a function of the amplitude of fluctuations for small amplitudes.

AN EXACTLY SOLVABLE ONE-DIMENSIONAL MODEL OF FERMIONS WITH CORRELATED HOPPING

1996 ◽  
Vol 10 (27) ◽  
pp. 3673-3683 ◽  
Author(s):  
IGOR N. KARNAUKHOV
Keyword(s):  
Critical Exponents ◽  
Ground State ◽  
Correlation Functions ◽  
State Energy ◽  
One Dimension ◽  
Supersymmetric Model ◽  
Dimensional Model ◽  
Long Distance ◽  
One Dimensional ◽  
Exactly Solvable

A new solution of supersymmetric model of electrons with correlated hopping which generalizes those obtained earlier is formulated. The model is solved in one dimension by the Bethe ansatz. The ground state energy is calculated, and the critical exponents describing the decrease of the correlation functions on long distance are derived.

Mixture of interacting supersymmetric spinless fermions and bosons in a one-dimensional trap

2016 ◽  
Vol 30 (25) ◽  
pp. 1630007 ◽  
Author(s):  
P. Schlottmann
Keyword(s):  
Gas Phase ◽  
Ground State ◽  
State Energy ◽  
Optical Trap ◽  
Interaction Strength ◽  
Finite Size ◽  
One Dimension ◽  
One Dimensional ◽  
Bethe Ansatz Solution ◽  
Finite Size Corrections

We consider a gas mixture consisting of spinless fermions and bosons in one dimension interacting via a repulsive [Formula: see text]-function potential. Bosons and fermions are assumed to have equal masses and the interaction strength between bosons and among bosons and fermions is the same. Using the Bethe ansatz solution of the model, we study the ground state properties, the dressed energy potentials for the two bands of rapidities, the elementary particle and hole excitations, the thermodynamics, the finite size corrections to the ground state energy leading to the conformal towers, and the asymptotic behavior at large distances of some relevant correlation functions. The low-energy excitations of the system form a two-component Luttinger liquid. In an elongated optical trap the gas phase separates as a function of the distance from the center of the trap.

All-Temperature Partition Function from Variationally Optimized Canonical Density Matrix

1983 ◽  
Vol 38 (12) ◽  
pp. 1373-1382
Author(s):  
R. Baltin
Keyword(s):  
Density Matrix ◽  
Ground State ◽  
Order Differential Equation ◽  
Bloch Equation ◽  
Mean Square ◽  
Spatial Variables ◽  
One Dimensional ◽  
Exactly Solvable ◽  
The Mean ◽  
The One

Abstract For the canonical density matrix C(r, r0,β) a variational ansatz C̄̄f = (1 - f̄) Ccl + f̄ Cgr is made where Ccl and Cgr are the classical and the ground state expressions which are exact in the high temperature (β → 0) and in the low-temperature limits (β → + ∞), respectively, and f̄ is a trial function subject to the restriction that f̄ → 0 for β → 0 and f̄ → 1 for β → ∞. With the approximation that f̄ be dependent only upon β, not upon spatial variables, the mean square error arising when Cf is inserted into the Bloch equation is made a minimum. The Euler equation for this variational problem is an ordinary second order differential equation for f̄=f(β) to be solved numerically. The method is tested for the exactly solvable case of the one dimensional harmonic oscillator.

PERELOMOV AND BARUT–GIRARDELLO SU(1, 1) COHERENT STATES FOR HARMONIC OSCILLATOR IN ONE-DIMENSIONAL HALF SPACE

2006 ◽  
Vol 21 (12) ◽  
pp. 2635-2644 ◽  
Author(s):  
Q. H. LIU ◽  
H. ZHUO
Keyword(s):  
Coherent State ◽  
Harmonic Oscillator ◽  
Half Space ◽  
Ground State ◽  
Classical Limit ◽  
Coherent States ◽  
Mean Values ◽  
One Dimensional ◽  
The Mean

The Perelomov and the Barut–Girardello SU(1, 1) coherent states for harmonic oscillator in one-dimensional half space are constructed. Results show that the uncertainty products ΔxΔp for these two coherent states are bound from below [Formula: see text] that is the uncertainty for the ground state, and the mean values for position x and momentum p in classical limit go over to their classical quantities respectively. In classical limit, the uncertainty given by Perelomov coherent does not vanish, and the Barut–Girardello coherent state reveals a node structure when positioning closest to the boundary x = 0 which has not been observed in coherent states for other systems.

DIFFUSION IN ONE-DIMENSIONAL DISORDERED LATTICE

2012 ◽  
Vol 26 (01) ◽  
pp. 1150011 ◽  
Author(s):  
P. K. HUNG ◽  
T. V. MUNG ◽  
N. V. HONG
Keyword(s):  
Diffusion Coefficient ◽  
Correlation Factor ◽  
One Dimensional ◽  
Uniform Distributions ◽  
Disordered Lattice ◽  
Specific Effects ◽  
The Mean ◽  
Mc Simulation ◽  
Mean Time ◽  
Good Agreement

The diffusion in one-dimensional (1D) lattices with different types of energetic disorders has been investigated using both analytical method and Monte Carlo (MC) simulation. In single-particle case of two-level and uniform distributions the calculation shows a good agreement between analytical and simulation results for certain diffusion quantities. The expression for temperature dependence of diffusion coefficient DS is not Arrhenius one, but it tends to have Arrhenius type in the regime of low temperature. For many-particle case the simulation revealed two specific effects: first effect concerning the correlation factor FM decreases the diffusion coefficient DM as the coverage increases, second one relating to the mean time between two consecutive hops τ jump M conversely increase DM. For all 1D lattices the diffusion coefficient decreases with the coverage due to that first effect is stronger than second one. Furthermore, we have demonstrated that the ratio DM/DS weakly depends on temperature, although FM/FS and τ jump M/τ jump S strongly vary in the considered temperature interval.

THERMODYNAMICS OF LOW-DENSITY ELECTRON GAS ON HIGHLY DISORDERED ONE-DIMENSIONAL HOST LATTICE

2004 ◽  
Vol 18 (20n21) ◽  
pp. 2863-2876
Author(s):  
V. SLAVIN ◽  
A. SLUTSKIN
Keyword(s):  
Spin Glasses ◽  
Electron Gas ◽  
Three Dimensional ◽  
Thermodynamic Characteristics ◽  
Host Lattice ◽  
Dimensional Electron ◽  
One Dimensional ◽  
Disordered Lattice ◽  
Dimensional Electron Gas ◽  
Computer Procedure

The low-temperature thermodynamics of a one-dimensional electron gas on a disordered lattice, which comes to existence when the inter-electron distances exceed noticeably the inter-site ones, has been studied. An efficient computer procedure, based on the presentation of the partition function as a product of random transfer-matrixes, has been developed for calculations of thermodynamic characteristics of the system under consideration. The lattice structures were varied from completely chaotic up to the strictly regular one. It has been established that for any degree of disorder the entropy and heat capacity of the system tend to zero linearly as the temperature is reduced. The conclusion about the gapless character of the elementary excitations spectrum has been made. An instability of one-dimensional electron gas on a disordered lattice has been revealed: under conditions of vanishingly small disordering of the lattice, the long-range order in the systems under consideration is broken by frustrations that are one-dimensional analogues of the frustrations in two- and three-dimensional spin glasses.

Self-interstitial Diffusion in α-Zirconium

2001 ◽  
Vol 677 ◽  
Author(s):  
W.J. Zhu ◽  
C.H. Woo
Keyword(s):  
Ground State ◽  
Diffusion Processes ◽  
Many Body ◽  
Interstitial Diffusion ◽  
One Dimensional ◽  
Mean Lifetime ◽  
Migration Mechanism ◽  
Out Of Plane ◽  
On Line ◽  
The Mean

ABSTRACTSelf-interstitial Diffusion in α-Zirconium-Zr is studied using Molecular Dynamic (MD) and molecular static (MS) simulation using Ackland's many-body inter-atomic potential. The basal crowdion configuration is found to be the ground state. The diffusion process in Zr is complex. Four types of diffusion jumps can be identified, two in-plane and two out-of plane. The in-plane migration mechanism is dominated by one-dimensional crowdion motion along the [1120] directions, interrupted by occasional out-of-plane and on-line or off-line jumps. The mean lifetime before rotation of the crowdion is reported as a function of temperature. The activation energies for the diffusion processes are obtained. The diffusional anisotropy factor Dc/Da is also obtained, and compares well with experiment results.

scholarly journals One-dimensional hydrogen atom

2016 ◽  
Vol 472 (2185) ◽  
pp. 20150534 ◽  
Author(s):  
Rodney Loudon
Keyword(s):  
Hydrogen Atom ◽  
Schrödinger Equation ◽  
Ground State ◽  
Short Distance ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
One Dimension ◽  
Current Status ◽  
One Dimensional ◽  
The One

The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.

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