scholarly journals Non-equilibrium scale invariance and shortcuts to adiabaticity in a one-dimensional Bose gas

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
W. Rohringer ◽  
D. Fischer ◽  
F. Steiner ◽  
I. E. Mazets ◽  
J. Schmiedmayer ◽  
...  
Keyword(s):  
Thermal State ◽  
Rapid Change ◽  
Rapid Expansion ◽  
Scale Invariant ◽  
Free Expansion ◽  
One Dimensional ◽  
Occupation Numbers ◽  
Shortcuts To Adiabaticity ◽  
External Trapping Potential ◽  
Density Correlations

Abstract We present experimental evidence for scale invariant behaviour of the excitation spectrum in phase-fluctuating quasi-1d Bose gases after a rapid change of the external trapping potential. Probing density correlations in free expansion, we find that the temperature of an initial thermal state scales with the spatial extension of the cloud as predicted by a model based on adiabatic rescaling of initial eigenmodes with conserved quasiparticle occupation numbers. Based on this result, we demonstrate that shortcuts to adiabaticity for the rapid expansion or compression of the gas do not induce additional heating.

scholarly journals Density-density correlations in a Luttinger liquid: Lattice approximation in the Calogero-Sutherland model

1999 ◽  
Vol 77 (5) ◽  
pp. 327-341 ◽  
Author(s):  
D Sen ◽  
R K Bhaduri
Keyword(s):  
Luttinger Liquid ◽  
Exact Results ◽  
Dimensional Model ◽  
Lattice Method ◽  
One Dimensional ◽  
Density Correlation ◽  
Time Correlations ◽  
Sutherland Model ◽  
Lattice Approximation ◽  
Density Correlations

For a one-dimensional model in which the two-body interactions are long-range and strong, the system almost crystallizes. The harmonic modes of such a lattice were used by Krivnov and Ovchinnikov to compute the ground-state wave function and the dynamical density-density correlations. We review this method, and apply it to the Calogero-Sutherland model, whose density-density correlation functions are exactly known for certain values of the coupling constant. We show numerically that the correlations obtained are quite accurate even if the coupling is not very large. Such comparisons have been made earlier by Forrester. The lattice method is considerably simpler than the ones used to derive the exact results, and yields expressions for the correlations- which are easily plotted. The equal-time correlations can be expanded in inverse powers of coupling; we show that the two leading order terms agree with the exact results which are known for integer values of the coupling. The strength-dependent power law fall-off is typical of a Luttinger liquid.In a general one-dimensional model where the two-body interaction decreases as a power of the relative distance, we argue, following Schulz, that at zero temperature the system behaves as a Luttinger liquid if the power exceeds 1, and as a Wigner crystal if it is less than 1.PACS Nos.: 63.20-e, 71.10Pm

scholarly journals Classical and Quantum Shortcuts to Adiabaticity for Scale-Invariant Driving

2014 ◽  
Vol 4 (2) ◽  
Author(s):  
Sebastian Deffner ◽  
Christopher Jarzynski ◽  
Adolfo del Campo
Keyword(s):  
Scale Invariant ◽  
Shortcuts To Adiabaticity

scholarly journals ALTERNATIVE CONFORMAL QUANTUM MECHANICS

2011 ◽  
Vol 26 (16) ◽  
pp. 2735-2742 ◽  
Author(s):  
S.-H. HO
Keyword(s):  
Quantum Mechanics ◽  
Conformal Invariance ◽  
Invariant Theory ◽  
Mechanical Model ◽  
Conformal Transformation ◽  
Quantum Mechanical ◽  
Scale Invariant ◽  
One Dimensional ◽  
Quantum Mechanical Model ◽  
Conformal Quantum Mechanics

We investigate a one-dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal transformation such that a scale invariant theory is also invariant under this new conformal transformation.

Scale-invariant initial value problems in one-dimensional dynamic elastoplasticity, with consequences for multidimensional nonassociative plasticity

1992 ◽  
Vol 3 (3) ◽  
pp. 225-254 ◽  
Author(s):  
David G. Schaeffer ◽  
Michael Shearer
Keyword(s):  
Gas Dynamics ◽  
Initial Conditions ◽  
Piecewise Linear ◽  
Flow Rule ◽  
Longitudinal Motion ◽  
Entropy Condition ◽  
Initial Value ◽  
Scale Invariant ◽  
One Dimensional ◽  
Dynamic Plasticity

This paper solves a class of one-dimensional, dynamic elastoplasticity problems for equations which describe the longitudinal motion of a rod. The initial conditions U(x, 0) are continuous and piecewise linear, the derivative ∂U/∂x(x, 0) having just one jump at x = 0. Both the equations and the initial data are invariant under the scaling Ũ(x, t) = α−1U(αx, αt), where α > 0; hence the term scale-invariant. Both in underlying motivation and in solution, this problem is highly analogous to the Riemann problem from gas dynamics. These ideas are applied to the Sandler–Rubin example of non-unique solutions in dynamic plasticity with a nonassociative flow rule. We introduce an entropy condition that re-establishes uniqueness, but we also exhibit problems regarding existence.

scholarly journals Finite one-dimensional impenetrable Bose systems: Occupation numbers

2003 ◽  
Vol 67 (4) ◽  
Author(s):  
P. J. Forrester ◽  
N. E. Frankel ◽  
T. M. Garoni ◽  
N. S. Witte
Keyword(s):  
One Dimensional ◽  
Occupation Numbers

scholarly journals Exact behavior of the energy density inside a one-dimensional oscillating cavity with a thermal state

2010 ◽  
Vol 374 (38) ◽  
pp. 3899-3907 ◽  
Author(s):  
Danilo T. Alves ◽  
Edney R. Granhen ◽  
Hector O. Silva ◽  
Mateus G. Lima
Keyword(s):  
Energy Density ◽  
Thermal State ◽  
One Dimensional
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