FINITE SIZE CORRECTIONS FOR MULTIPARTICLE SPIN-½ NONLINEAR SCHRÖDINGER MODEL

1991 ◽  
Vol 05 (23) ◽  
pp. 1603-1606
Author(s):  
YI-MIN LIU ◽  
FU-CHO PU ◽  
HANG SU
Keyword(s):  
Critical Point ◽  
Ground State ◽  
Finite Size ◽  
Conformal Anomaly ◽  
Nonlinear Schrödinger ◽  
Size Correction ◽  
Finite Size Correction ◽  
Finite Size Corrections ◽  
Maclaurin Formula

Applied Euler-Maclaurin formula, we compute the finite size correction to the energy of the ground state for the Spin-½ Nonlinear Schrödinger model. We get conformal anomaly for this model at the critical point (T=0).

FINITE SIZE CORRECTION ON THE SURFACE WIDTH OF RANDOM DEPOSITION WITH SURFACE RELAXATION MODEL

2006 ◽  
Vol 20 (21) ◽  
pp. 3057-3070
Author(s):  
A. A. MASOUDI ◽  
R. ZARGINI
Keyword(s):  
Fourier Transformation ◽  
Finite Size ◽  
Surface Relaxation ◽  
Nonlinear Coupling ◽  
Relaxation Model ◽  
Coupling Constant ◽  
The Mean ◽  
Size Correction ◽  
Finite Size Correction ◽  
Finite Size Corrections

The Kardar–Parizi–Zhang equation for surface growth has been analyzed in the regime where the nonlinear coupling constant, λ, is small (Edwards–Wilkinson equation). By using the Fourier transformation the finite size corrections on the mean-square width could be calculated. It is found that the calculated interface width for [Formula: see text] behaves as [Formula: see text] and for [Formula: see text] behaves like [Formula: see text].

scholarly journals NUMERICAL STUDY OF CHARGE AND STATISTICS OF LAUGHLIN QUASIPARTICLES

1999 ◽  
Vol 14 (04) ◽  
pp. 537-557 ◽  
Author(s):  
HEIDI KJØNSBERG ◽  
JAN MYRHEIM
Keyword(s):  
Numerical Study ◽  
Finite Size ◽  
Expected Value ◽  
Wave Functions ◽  
Numerical Calculations ◽  
Filling Fraction ◽  
Slow Convergence ◽  
Berry Phases ◽  
Size Correction ◽  
Finite Size Correction

We present numerical calculations of the charge and statistics, as extracted from Berry phases, of the Laughlin quasiparticles, near filling fraction 1/3, and for system sizes of up to 200 electrons. For the quasiholes our results confirm that the charge and statistics parameter are e/3 and 1/3, respectively. For the quasielectron charge we find a slow convergence towards the expected value of -e/3, with a finite size correction for N electrons of approximately -0.13e/N. The statistics parameter for the quasielectrons has no well defined value even for 200 electrons, but might possibly converge to 1/3. The anyon model works well for the quasiholes, but requires singular two-anyon wave functions for modelling two Laughlin quasielectrons.

Finite Heisenberg Quantum Spin Chain

2019 ◽  
pp. 667-686
Author(s):  
Hans-Peter Eckle
Keyword(s):  
Bethe Ansatz ◽  
Conformal Symmetry ◽  
Finite Size ◽  
Quantum Spin ◽  
Ansatz Method ◽  
Finite Sums ◽  
Mathematical Techniques ◽  
Higher Order Corrections ◽  
Finite Size Corrections ◽  
Maclaurin Formula

The Bethe ansatz genuinely considers a finite system. The extraction of finite-size results from the Bethe ansatz equations is of genuine interest, especially against the background of the results of finite-size scaling and conformal symmetry in finite geometries. The mathematical techniques introduced in chapter 19 permit a systematic treatment in this chapter of finite-size corrections as corrections to the thermodynamic limit of the system. The application of the Euler-Maclaurin formula transforming finite sums into integrals and finite-size corrections transforms the Bethe ansatz equations into Wiener–Hopf integral equations with inhomogeneities representing the finite-size corrections solvable using the Wiener–Hopf technique. The results can be compared to results for finite systems obtained from other approaches that are independent of the Bethe ansatz method. It briefly discusses higher-order corrections and offers a general assessment of the finite-size method.

scholarly journals Finite-size correction in a disordered system: A new divergence

1995 ◽  
Vol 52 (5) ◽  
pp. 4860-4864 ◽  
Author(s):  
Somendra M. Bhattacharjee ◽  
Sutapa Mukherji
Keyword(s):  
Finite Size ◽  
Disordered System ◽  
System A ◽  
Size Correction ◽  
Finite Size Correction

A GLUON PLASMA GIANT RESONANCE AND COLOR-SINGLETNESS AT FINITE TEMPERATURE

1999 ◽  
Vol 14 (29) ◽  
pp. 2003-2010
Author(s):  
LINA PARIA ◽  
AFSAR ABBAS ◽  
M. G. MUSTAFA
Keyword(s):  
Finite Temperature ◽  
Giant Resonance ◽  
Finite Size ◽  
Gluon Plasma ◽  
System A ◽  
Size Correction ◽  
Finite Size Correction

By imposing the SU(3) color-singletness constraint on a gluonic system, a heavy gluon–plasma giant resonance is shown to arise at finite temperature. This is made possible through the proper incorporation of the finite size correction brought in by the color-singletness restriction.

scholarly journals Motions of the String Solutions in the XXZ Spin Chain Under a Varying Twist

1997 ◽  
Vol 12 (04) ◽  
pp. 801-838 ◽  
Author(s):  
N. Fumita ◽  
H. Itoyama ◽  
T. Oota
Keyword(s):  
Ground State ◽  
Spin Chain ◽  
Imaginary Axis ◽  
Berry Phase ◽  
Numerical Study ◽  
Twist Angle ◽  
Finite Size ◽  
Bound State ◽  
Branch Points ◽  
Finite Size Corrections

We determine the motions of the roots of the Bethe ansatz equation for the ground state in the XXZ spin chain under a varying twist angle. This is done by analytic as well as numerical study in a finite size system. In the attractive critical regime 0 < Δ < 1, we reveal intriguing motions of strings due to the finite size corrections to the length of the strings: in the case of two-strings, the roots collide into the branch points perpendicularly to the imaginary axis, while in the case of three-strings, they fluctuate around the center of the string. These are successfully generalized to the case of n-string. These results are used to determine the final configuration of the momenta as well as that of the phase shift functions. We obtain these as well as the period and the Berry phase in the regime Δ ≤ -1 also, establishing the continuity of the previous results at -1 < Δ < 0 to this regime. We argue that the Berry phase can be used as a measure of the statistics of the quasiparticle (or the bound state) involved in the process.

Finite-size corrections to Poisson approximations of rare events in renewal processes

2001 ◽  
Vol 38 (02) ◽  
pp. 554-569 ◽  
Author(s):  
John L. Spouge
Keyword(s):  
Renewal Process ◽  
Point Processes ◽  
Correction Term ◽  
Rare Event ◽  
Finite Size ◽  
Time Interval ◽  
Renewal Processes ◽  
Size Correction ◽  
Renewal Events ◽  
Finite Size Corrections

Consider a renewal process. The renewal events partition the process into i.i.d. renewal cycles. Assume that on each cycle, a rare event called 'success’ can occur. Such successes lend themselves naturally to approximation by Poisson point processes. If each success occurs after a random delay, however, Poisson convergence may be relatively slow, because each success corresponds to a time interval, not a point. In 1996, Altschul and Gish proposed a finite-size correction to a particular approximation by a Poisson point process. Their correction is now used routinely (about once a second) when computers compare biological sequences, although it lacks a mathematical foundation. This paper generalizes their correction. For a single renewal process or several renewal processes operating in parallel, this paper gives an asymptotic expansion that contains in successive terms a Poisson point approximation, a generalization of the Altschul-Gish correction, and a correction term beyond that.

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