9 research outputs found
Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath
We derive a Lindblad master equation that approximates the dynamics of a
Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying
the time evolution of operators under the adjoint master equation we prove
that, for large system sizes, these operators attain their thermal equilibrium
expectation values in the long-time limit, and we calculate the rate at which
these values are approached. Integrability of the LMG model prevents
thermalization in the absence of a bath, and our work provides an explicit
proof that the bath indeed restores thermalization. Imposing thermalization on
this otherwise non-thermalizing model outlines an avenue towards probing the
unconventional thermodynamic properties predicted to occur in
ultracold-atom-based realizations of the LMG model.Comment: 10 pages, 3 figure
The entropy of dense non-commutative fermion gases
We investigate the properties of two- and three-dimensional non-commutative
fermion gases with fixed total z-component of angular momentum, J_z, and at
high density for the simplest form of non-commutativity involving constant
spatial commutators. Analytic expressions for the entropy and pressure are
found. The entropy exhibits non-extensive behaviour while the pressure reveals
the presence of incompressibility in two, but not in three dimensions.
Remarkably, for two-dimensional systems close to the incompressible density,
the entropy is proportional to the square root of the system size, i.e., for
such systems the number of microscopic degrees of freedom is determined by the
circumference, rather than the area (size) of the system. The absence of
incompressibility in three dimensions, and subsequently also the absence of a
scaling law for the entropy analogous to the one found in two dimensions, is
attributed to the form of the non-commutativity used here, the breaking of the
rotational symmetry it implies and the subsequent constraint on J_z, rather
than the angular momentum J. Restoring the rotational symmetry while
constraining the total angular momentum J seems to be crucial for
incompressibility in three dimensions. We briefly discuss ways in which this
may be done and point out possible obstacles.Comment: 15 pages, 10 figure
Universal cooling dynamics towards a quantum critical point
We investigate the loss of adiabaticity when cooling a many-body quantum
system from an initial thermal state towards a quantum critical point. The
excitation density, which quantifies the degree of adiabaticity of the
dynamics, is found to obey scaling laws in the cooling velocity as well as in
the initial and final temperatures of the cooling protocol. The scaling laws
are universal, governed by the critical exponents of the quantum phase
transition. The validity of these statements is shown analytically for a Kitaev
quantum wire coupled to Markovian baths, and subsequently argued to be valid
under rather general conditions. Our results establish that quantum critical
properties can be probed dynamically at finite temperature, without even
varying the control parameter of the quantum phase transitions.Comment: 5+4 pages, 2+2 figures; companion paper to "Long-range Kitaev chain
in a thermal bath: Analytic techniques for time-dependent systems and
environments" by the same authors and submitted on the same da
Adiabatic quantum trajectories in engineered reservoirs
We analyze the efficiency of protocols for adiabatic quantum state transfer
assisted by an engineered reservoir. The target dynamics is a quantum
trajectory in the Hilbert space and is the fixed point of a time-dependent
master equation. We specialize to quantum state transfer in a qubit and
determine the optimal schedule for a class of time-dependent Lindblad
equations. The speed limit on state transfer is extracted from a physical model
of a qubit coupled to a reservoir, from which the Lindblad equation is derived
in the Born-Markov limit. Our analysis shows that the resulting efficiency is
comparable to the efficiency of the optimal unitary dynamics. Numerical studies
indicate that reservoir-engineered protocols could outperform unitary protocols
outside the regime of the Born-Markov master equation, namely, when
correlations between the qubit and reservoir become relevant. Our study
contributes to the theory of shortcuts to adiabaticity for open quantum systems
and to the toolbox of protocols of the NISQ era.Comment: 14+7 pages, 7 figure
Guidelines for Quality Management of Apallic Syndrome / Vegetative State.
Item does not contain fulltex