224 research outputs found
Regression relation for pure quantum states and its implications for efficient computing
We obtain a modified version of the Onsager regression relation for the
expectation values of quantum-mechanical operators in pure quantum states of
isolated many-body quantum systems. We use the insights gained from this
relation to show that high-temperature time correlation functions in many-body
quantum systems can be controllably computed without complete diagonalization
of the Hamiltonians, using instead the direct integration of the Schroedinger
equation for randomly sampled pure states. This method is also applicable to
quantum quenches and other situations describable by time-dependent many-body
Hamiltonians. The method implies exponential reduction of the computer memory
requirement in comparison with the complete diagonalization. We illustrate the
method by numerically computing infinite-temperature correlation functions for
translationally invariant Heisenberg chains of up to 29 spins 1/2. Thereby, we
also test the spin diffusion hypothesis and find it in a satisfactory agreement
with the numerical results. Both the derivation of the modified regression
relation and the justification of the computational method are based on the
notion of quantum typicality.Comment: 16 pages, 4 figures; minor textual corrections; parts rearrange
Hilbert Space Average Method and adiabatic quantum search
We discuss some aspects related to the so-called Hilbert space Average
Method, as an alternative to describe the dynamics of open quantum systems.
First we present a derivation of the method which does not make use of the
algebra satisfied by the operators involved in the dynamics, and extend the
method to systems subject to a Hamiltonian that changes with time. Next we
examine the performance of the adiabatic quantum search algorithm with a
particular model for the environment. We relate our results to the criteria
discussed in the literature for the validity of the above-mentioned method for
similar environments.Comment: 6 pages, 1 figur
Quantum discord and local demons
Quantum discord was proposed as a measure of the "quantumness" of
correlations. There are at least three different discord-like quantities, two
of which determine the difference between the efficiencies of a Szilard's
engine under different sets of restrictions. The three discord measures vanish
simulataneosly. We introduce an easy way to test for zero discord, relate it to
the Cerf-Adami conditional entropy and show that there is no relation between
the discord and the local disitnguishability.Comment: 7 pages, RevTeX. Some minor changes after comments from colleagues,
some references added. Similar to published versio
Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics
We solve the Schroedinger equation for an interacting spin-chain locally
coupled to a quantum environment with a specific degeneracy structure. The
reduced dynamics of the whole spin-chain as well as of single spins is
analyzed. We show, that the total spin-chain relaxes to a thermal equilibrium
state independently of the internal interaction strength. In contrast, the
asymptotic states of each individual spin are thermal for weak but non-thermal
for stronger spin-spin coupling. The transition between both scenarios is found
for couplings of the order of , with denoting
the Zeeman-splitting. We compare these results with a master equation
treatment; when time averaged, both approaches lead to the same asymptotic
state and finally with analytical results.Comment: RevTeX, 8 pages, 14 figures, added DOI and forgotten reference
Quantum equilibration in finite time
It has recently been shown that small quantum subsystems generically
equilibrate, in the sense that they spend most of the time close to a fixed
equilibrium state. This relies on just two assumptions: that the state is
spread over many different energies, and that the Hamiltonian has
non-degenerate energy gaps. Given the same assumptions, it has also been shown
that closed systems equilibrate with respect to realistic measurements. We
extend these results in two important ways. First, we prove equilibration over
a finite (rather than infinite) time-interval, allowing us to bound the
equilibration time. Second, we weaken the non degenerate energy gaps condition,
showing that equilibration occurs provided that no energy gap is hugely
degenerate.Comment: 7 page
Thermalisation of Local Observables in Small Hubbard Lattices
We present a study of thermalisation of a small isolated Hubbard lattice
cluster prepared in a pure state with a well-defined energy. We examine how a
two-site subsystem of the lattice thermalises with the rest of the system as
its environment. We explore numerically the existence of thermalisation over a
range of system parameters, such as the interaction strength, system size and
the strength of the coupling between the subsystem and the rest of the lattice.
We find thermalisation over a wide range of parameters and that interactions
are crucial for efficient thermalisation of small systems. We relate this
thermalisation behaviour to the eigenstate thermalisation hypothesis and
quantify numerically the extent to which eigenstate thermalisation holds. We
also verify our numerical results theoretically with the help of previously
established results from random matrix theory for the local density of states,
particularly the finite-size scaling for the onset of thermalisation.Comment: 22 pages, 23 figure
Correlated projection operator approach to non-Markovian dynamics in spin baths
The dynamics of an open quantum system is usually studied by performing a
weak-coupling and weak-correlation expansion in the system-bath interaction.
For systems exhibiting strong couplings and highly non-Markovian behavior this
approach is not justified. We apply a recently proposed correlated projection
superoperator technique to the model of a central spin coupled to a spin bath
via full Heisenberg interaction. Analytical solutions to both the
Nakajima-Zwanzig and the time-convolutionless master equation are determined
and compared with the results of the exact solution. The correlated projection
operator technique significantly improves the standard methods and can be
applied to many physical problems such as the hyperfine interaction in a
quantum dot
Robustness of Highly Entangled Multi-Qubit States Under Decoherence
We investigate the decay of entanglement, due to decoherence, of multi-qubit
systems that are initially prepared in highly (in some cases maximally)
entangled states. We assume that during the decoherence processes each qubit of
the system interacts with its own, independent environment. We determine, for
systems with a small number of qubits and for various decoherence channels, the
initial states exhibiting the most robust entanglement. We also consider a
restricted version of this robustness optimization problem, only involving
states equivalent under local unitary transformations to the |GHZ> state.Comment: 16 pages, 3 figures. Changes in Sec.
Local temperature in quantum thermal states
We consider blocks of quantum spins in a chain at thermal equilibrium,
focusing on their properties from a thermodynamical perspective. Whereas in
classical systems the temperature behaves as an intensive magnitude, a
deviation from this behavior is expected in quantum systems. In particular, we
see that under some conditions the description of the blocks as thermal states
with the same global temperature as the whole chain fails. We analyze this
issue by employing the quantum fidelity as a figure of merit, singling out in
detail the departure from the classical behavior. The influence in this sense
of zero-temperature quantum phase transitions can be clearly observed within
this approach. Then we show that the blocks can be considered indeed as thermal
states with a high fidelity, provided an effective local temperature is
properly identified. Such a result originates from typical properties of
reduced sub-systems of energy-constrained Hilbert spaces. Finally, the relation
between local and global temperature is analyzed as a function of the size of
the blocks and the system parameters.Comment: 10 pages, 10 figures. New fidelity measure with similar result
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