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 Nonadiabatic Energy Fluctuations of Scale-Invariant Quantum Systems in a Time-Dependent Trap

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 515
Author(s):  
Mathieu Beau ◽  
Adolfo del Campo
Keyword(s):  
Quantum Fluids ◽  
Time Dependent ◽  
Many Body ◽  
Scale Invariant ◽  
Exact Relation ◽  
Shortcuts To Adiabaticity ◽  
Initial Expectation ◽  
Unitary Fermi Gas ◽  
Sutherland Model ◽  
The One

We consider the nonadiabatic energy fluctuations of a many-body system in a time-dependent harmonic trap. In the presence of scale-invariance, the dynamics becomes self-similar and the nondiabatic energy fluctuations can be found in terms of the initial expectation values of the second moments of the Hamiltonian, square position, and squeezing operators. Nonadiabatic features are expressed in terms of the scaling factor governing the size of the atomic cloud, which can be extracted from time-of-flight images. We apply this exact relation to a number of examples: the single-particle harmonic oscillator, the one-dimensional Calogero-Sutherland model, describing bosons with inverse-square interactions that includes the non-interacting Bose gas and the Tonks-Girdardeau gas as limiting cases, and the unitary Fermi gas. We illustrate these results for various expansion protocols involving sudden quenches of the trap frequency, linear ramps and shortcuts to adiabaticity. Our results pave the way to the experimental study of nonadiabatic energy fluctuations in driven quantum fluids.

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.

Scale-Invariant Theory of Optical Properties of Fractal Clusters

1990 ◽  
Author(s):  
Vadim A. Markel ◽  
Leonid S. Muratov ◽  
Mark I. Stockman ◽  
Thomas F. George
Keyword(s):  
Optical Properties ◽  
Invariant Theory ◽  
Scale Invariant ◽  
Fractal Clusters

Best Matching: Technical Details

2018 ◽  
Author(s):  
Flavio Mercati
Keyword(s):  
Point Particle ◽  
Euclidean Group ◽  
Scale Invariant ◽  
Similarity Group ◽  
N Body Problem ◽  
Technical Details ◽  
Matching Procedure ◽  
Principal Fibre ◽  
Principal Fibre Bundle ◽  
Gauge Connection

The best matching procedure described in Chapter 4 is equivalent to the introduction of a principal fibre bundle in configuration space. Essentially one introduces a one-dimensional gauge connection on the time axis, which is a representation of the Euclidean group of rotations and translations (or, possibly, the similarity group which includes dilatations). To accommodate temporal relationalism, the variational principle needs to be invariant under reparametrizations. The simplest way to realize this in point–particle mechanics is to use Jacobi’s reformulation of Mapertuis’ principle. The chapter concludes with the relational reformulation of the Newtonian N-body problem (and its scale-invariant variant).

Sign in / Sign up

Export Citation Format

Share Document