561 research outputs found
Shortening the order of paraunitary matrices in SBR2 algorithm
The second order sequential best rotation (SBR2) algorithm has recently been proposed as a very effective tool in decomposing a para-Hermitian polynomial matrix R(z) into a diagonal polynomial matrix T(z) and a paraunitary matrix B(,z), extending the eigenvalue decomposition to polynomial matrices, R-(z) = B(z)T(z)~B(z). However, the algorithm results in polynomials of very high order, which limits its applicability. Therefore, in this paper we evaluate approaches to reduce the order of the paraunitary matrices, either within each step of SBR2, or after convergence. The paraunitary matrix B(z) is replaced by a near-paraunitary quantity BN(z), whose error will be assessed. Simulation results show that the proposed truncation can greatly reduce the polynomial order while retaining good near-paraunitariness of BN(z)
Low-temperature dynamical simulation of spin-boson systems
The dynamics of spin-boson systems at very low temperatures has been studied
using a real-time path-integral simulation technique which combines a
stochastic Monte Carlo sampling over the quantum fluctuations with an exact
treatment of the quasiclassical degrees of freedoms. To a large degree, this
special technique circumvents the dynamical sign problem and allows the
dynamics to be studied directly up to long real times in a numerically exact
manner. This method has been applied to two important problems: (1) crossover
from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the
zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K
is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure
Local time and the pricing of time-dependent barrier options
A time-dependent double-barrier option is a derivative security that delivers
the terminal value at expiry if neither of the continuous
time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time
interval . Using a probabilistic approach we obtain a decomposition of
the barrier option price into the corresponding European option price minus the
barrier premium for a wide class of payoff functions , barrier functions
and linear diffusions . We show that the barrier
premium can be expressed as a sum of integrals along the barriers of
the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair
of functions solves a system of Volterra integral
equations of the first kind. We find a semi-analytic solution for this system
in the case of constant double barriers and briefly discus a numerical
algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic
Decoherence Strength of Multiple Non-Markovian Environments
It is known that one can characterize the decoherence strength of a Markovian
environment by the product of its temperature and induced damping, and order
the decoherence strength of multiple environments by this quantity. We show
that for non-Markovian environments in the weak coupling regime there also
exists a natural (albeit partial) ordering of environment-induced
irreversibility within a perturbative treatment. This measure can be applied to
both low-temperature and non-equilibrium environments.Comment: 6 pages, 1 figure, v3 included figure, appendix, and clarification of
result
Exact analytical solutions to the master equation of quantum Brownian motion for a general environment
We revisit the model of a quantum Brownian oscillator linearly coupled to an
environment of quantum oscillators at finite temperature. By introducing a
compact and particularly well-suited formulation, we give a rather quick and
direct derivation of the master equation and its solutions for general spectral
functions and arbitrary temperatures. The flexibility of our approach allows
for an immediate generalization to cases with an external force and with an
arbitrary number of Brownian oscillators. More importantly, we point out an
important mathematical subtlety concerning boundary-value problems for
integro-differential equations which led to incorrect master equation
coefficients and impacts on the description of nonlocal dissipation effects in
all earlier derivations. Furthermore, we provide explicit, exact analytical
results for the master equation coefficients and its solutions in a wide
variety of cases, including ohmic, sub-ohmic and supra-ohmic environments with
a finite cut-off.Comment: 37 pages (26 + appendices), 14 figures; this paper is an evolution of
arXiv:0705.2766v1, but contains far more general and significant results; v2
minor changes, double column, improved Appendix
Exactly solvable model of quantum diffusion
We study the transport property of diffusion in a finite translationally
invariant quantum subsystem described by a tight-binding Hamiltonian with a
single energy band and interacting with its environment by a coupling in terms
of correlation functions which are delta-correlated in space and time. For weak
coupling, the time evolution of the subsystem density matrix is ruled by a
quantum master equation of Lindblad type. Thanks to the invariance under
spatial translations, we can apply the Bloch theorem to the subsystem density
matrix and exactly diagonalize the time evolution superoperator to obtain the
complete spectrum of its eigenvalues, which fully describe the relaxation to
equilibrium. Above a critical coupling which is inversely proportional to the
size of the subsystem, the spectrum at given wavenumber contains an isolated
eigenvalue describing diffusion. The other eigenvalues rule the decay of the
populations and quantum coherences with decay rates which are proportional to
the intensity of the environmental noise. On the other hand, an analytical
expression is obtained for the dispersion relation of diffusion. The diffusion
coefficient is proportional to the square of the width of the energy band and
inversely proportional to the intensity of the environmental noise because
diffusion results from the perturbation of quantum tunneling by the
environmental fluctuations in this model. Diffusion disappears below the
critical coupling.Comment: Submitted to J. Stat. Phy
Toward scalable quantum computation with cavity QED systems
We propose a scheme for quantum computing using high-Q cavities in which the
qubits are represented by single cavity modes restricted in the space spanned
by the two lowest Fock states. We show that single qubit operations and
universal multiple qubit gates can be implemented using atoms sequentially
crossing the cavities.Comment: 14 pages, 8 figure
Weak-Localization in Chaotic Versus Non-Chaotic Cavities: A Striking Difference in the Line Shape
We report experimental evidence that chaotic and non-chaotic scattering
through ballistic cavities display distinct signatures in quantum transport. In
the case of non-chaotic cavities, we observe a linear decrease in the average
resistance with magnetic field which contrasts markedly with a Lorentzian
behavior for a chaotic cavity. This difference in line-shape of the
weak-localization peak is related to the differing distribution of areas
enclosed by electron trajectories. In addition, periodic oscillations are
observed which are probably associated with the Aharonov-Bohm effect through a
periodic orbit within the cavities.Comment: 4 pages revtex + 4 figures on request; amc.hub.94.
Breakdown of the Landauer bound for information erasure in the quantum regime
A known aspect of the Clausius inequality is that an equilibrium system
subjected to a squeezing \d S of its entropy must release at least an amount
|\dbarrm Q|=T|\d S| of heat. This serves as a basis for the Landauer
principle, which puts a lower bound for the heat generated by erasure
of one bit of information. Here we show that in the world of quantum
entanglement this law is broken. A quantum Brownian particle interacting with
its thermal bath can either generate less heat or even {\it adsorb} heat during
an analogous squeezing process, due to entanglement with the bath. The effect
exists even for weak but fixed coupling with the bath, provided that
temperature is low enough. This invalidates the Landauer bound in the quantum
regime, and suggests that quantum carriers of information can be much more
efficient than assumed so far.Comment: 13 pages, revtex, 2 eps figure
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