17,583 research outputs found
Fourth Order Algorithms for Solving the Multivariable Langevin Equation and the Kramers Equation
We develop a fourth order simulation algorithm for solving the stochastic
Langevin equation. The method consists of identifying solvable operators in the
Fokker-Planck equation, factorizing the evolution operator for small time steps
to fourth order and implementing the factorization process numerically. A key
contribution of this work is to show how certain double commutators in the
factorization process can be simulated in practice. The method is general,
applicable to the multivariable case, and systematic, with known procedures for
doing fourth order factorizations. The fourth order convergence of the
resulting algorithm allowed very large time steps to be used. In simulating the
Brownian dynamics of 121 Yukawa particles in two dimensions, the converged
result of a first order algorithm can be obtained by using time steps 50 times
as large. To further demostrate the versatility of our method, we derive two
new classes of fourth order algorithms for solving the simpler Kramers equation
without requiring the derivative of the force. The convergence of many fourth
order algorithms for solving this equation are compared.Comment: 19 pages, 2 figure
Coherence and Decoherence in Biological Systems: Principles of Noise Assisted Transport and the Origin of Long-lived Coherences
The quantum dynamics of transport networks in the presence of noisy
environments have recently received renewed attention with the discovery of
long-lived coherences in different photosynthetic complexes. This experimental
evidence has raised two fundamental questions: Firstly, what are the mechanisms
supporting long-lived coherences and secondly, how can we assess the possible
functional role that the interplay of noise and quantum coherence might play in
the seemingly optimal operation of biological systems under natural conditions?
Here we review recent results, illuminate them at the hand of two paradigmatic
systems, the Fenna-Matthew-Olson (FMO) complex and the light harvesting complex
LHII, and present new progress on both questions. In particular we introduce
the concept of the phonon antennae and discuss the possible microscopic origin
or long-lived electronic coherences.Comment: Paper delivered at the Royal Society Discussion Meeting
"Quantum-coherent energy transfer: implications for biology and new energy
technologies", 27 - 28 April 2011 at The Kavli Royal Society International
Centre, Buckinghamshire, UK. Accepted for publication in Philosophical
Transactions of the Royal Society
Any order imaginary time propagation method for solving the Schrodinger equation
The eigenvalue-function pair of the 3D Schr\"odinger equation can be
efficiently computed by use of high order, imaginary time propagators. Due to
the diffusion character of the kinetic energy operator in imaginary time,
algorithms developed so far are at most fourth-order. In this work, we show
that for a grid based algorithm, imaginary time propagation of any even order
can be devised on the basis of multi-product splitting. The effectiveness of
these algorithms, up to the 12 order, is demonstrated by computing
all 120 eigenstates of a model C molecule to very high precisions. The
algorithms are particularly useful when implemented on parallel computer
architectures.Comment: 8 pages, 3 figure
Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
We study fermionic pairing in an ultracold two-component gas of Li atoms
by observing an energy gap in the radio-frequency excitation spectra. With
control of the two-body interactions via a Feshbach resonance we demonstrate
the dependence of the pairing gap on coupling strength, temperature, and Fermi
energy. The appearance of an energy gap with moderate evaporative cooling
suggests that our full evaporation brings the strongly interacting system deep
into a superfluid state.Comment: 18 pages, 3 figure
Ultracold molecules: vehicles to scalable quantum information processing
We describe a novel scheme to implement scalable quantum information
processing using Li-Cs molecular state to entangle Li and Cs
ultracold atoms held in independent optical lattices. The Li atoms will
act as quantum bits to store information, and Cs atoms will serve as
messenger bits that aid in quantum gate operations and mediate entanglement
between distant qubit atoms. Each atomic species is held in a separate optical
lattice and the atoms can be overlapped by translating the lattices with
respect to each other. When the messenger and qubit atoms are overlapped,
targeted single spin operations and entangling operations can be performed by
coupling the atomic states to a molecular state with radio-frequency pulses. By
controlling the frequency and duration of the radio-frequency pulses,
entanglement can either be created or swapped between a qubit messenger pair.
We estimate operation fidelities for entangling two distant qubits and discuss
scalability of this scheme and constraints on the optical lattice lasers
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