5,858 research outputs found
High order Chin actions in path integral Monte Carlo
High order actions proposed by Chin have been used for the first time in path
integral Monte Carlo simulations. Contrarily to the Takahashi-Imada action,
which is accurate to fourth order only for the trace, the Chin action is fully
fourth order, with the additional advantage that the leading fourth and sixth
order error coefficients are finely tunable. By optimizing two free parameters
entering in the new action we show that the time step error dependence achieved
is best fitted with a sixth order law. The computational effort per bead is
increased but the total number of beads is greatly reduced, and the efficiency
improvement with respect to the primitive approximation is approximately a
factor of ten. The Chin action is tested in a one-dimensional harmonic
oscillator, a H drop, and bulk liquid He. In all cases a sixth-order
law is obtained with values of the number of beads that compare well with the
pair action approximation in the stringent test of superfluid He.Comment: 19 pages, 8 figure
The Boltzmann factor, DNA melting, and Brownian ratchets: Topics in an introductory physics sequence for biology and premedical students
Three, interrelated biologically-relevant examples of biased random walks are
presented: (1) A model for DNA melting, modelled as DNA unzipping, which
provides a way to illustrate the role of the Boltzmann factor in a venue
well-known to biology and pre-medical students; (2) the activity of helicase
motor proteins in unzipping double-stranded DNA, for example, at the
replication fork, which is an example of a Brownian ratchet; (3) force
generation by actin polymerization, which is another Brownian ratchet, and for
which the force and actin-concentration dependence of the velocity of actin
polymerization is determined
The Logic behind Feynman's Paths
The classical notions of continuity and mechanical causality are left in
order to refor- mulate the Quantum Theory starting from two principles: I) the
intrinsic randomness of quantum process at microphysical level, II) the
projective representations of sym- metries of the system. The second principle
determines the geometry and then a new logic for describing the history of
events (Feynman's paths) that modifies the rules of classical probabilistic
calculus. The notion of classical trajectory is replaced by a history of
spontaneous, random an discontinuous events. So the theory is reduced to
determin- ing the probability distribution for such histories according with
the symmetries of the system. The representation of the logic in terms of
amplitudes leads to Feynman rules and, alternatively, its representation in
terms of projectors results in the Schwinger trace formula.Comment: 15 pages, contribution to Mario Castagnino Festschrif
Propagation of Vortex Electron Wave Functions in a Magnetic Field
The physics of coherent beams of photons carrying axial orbital angular
momentum (OAM) is well understood and such beams, sometimes known as vortex
beams, have found applications in optics and microscopy. Recently electron
beams carrying very large values of axial OAM have been generated. In the
absence of coupling to an external electromagnetic field the propagation of
such vortex electron beams is virtually identical mathematically to that of
vortex photon beams propagating in a medium with a homogeneous index of
refraction. But when coupled to an external electromagnetic field the
propagation of vortex electron beams is distinctly different from photons. Here
we use the exact path integral solution to Schrodingers equation to examine the
time evolution of an electron wave function carrying axial OAM. Interestingly
we find that the nonzero OAM wave function can be obtained from the zero OAM
wave function, in the case considered here, simply by multipling it by an
appropriate time and position dependent prefactor. Hence adding OAM and
propagating can in this case be replaced by first propagating then adding OAM.
Also, the results shown provide an explicit illustration of the fact that the
gyromagnetic ratio for OAM is unity. We also propose a novel version of the
Bohm-Aharonov effect using vortex electron beams.Comment: 14 pages, 2 figures, submitted to Phys Rev
Entangling ability of a beam splitter in the presence of temporal which-path information
We calculate the amount of polarization-entanglement induced by two-photon
interference at a lossless beam splitter. Entanglement and its witness are
quantified respectively by concurrence and the Bell-CHSH parameter. In the
presence of a Mandel dip, the interplay of two kinds of which-path information
-- temporal and polarization -- gives rise to the existence of entangled
polarization-states that cannot violate the Bell-CHSH inequality.Comment: 8 pages including 2 figure
Heat Fluctuations in Brownian Transducers
Heat fluctuation probability distribution function in Brownian transducers
operating between two heat reservoirs is studied. We find, both analytically
and numerically, that the recently proposed Fluctuation Theorem for Heat
Exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)]
has to be modified when the coupling mechanism between both baths is
considered. We also extend such relation when external work is present. Our
work fixes the domain of applicability of the theorem in more realistic
operating systems.Comment: Comments are welcom
Realizable Hamiltonians for Universal Adiabatic Quantum Computers
It has been established that local lattice spin Hamiltonians can be used for
universal adiabatic quantum computation. However, the 2-local model
Hamiltonians used in these proofs are general and hence do not limit the types
of interactions required between spins. To address this concern, the present
paper provides two simple model Hamiltonians that are of practical interest to
experimentalists working towards the realization of a universal adiabatic
quantum computer. The model Hamiltonians presented are the simplest known
QMA-complete 2-local Hamiltonians. The 2-local Ising model with 1-local
transverse field which has been realized using an array of technologies, is
perhaps the simplest quantum spin model but is unlikely to be universal for
adiabatic quantum computation. We demonstrate that this model can be rendered
universal and QMA-complete by adding a tunable 2-local transverse XX coupling.
We also show the universality and QMA-completeness of spin models with only
1-local Z and X fields and 2-local ZX interactions.Comment: Paper revised and extended to improve clarity; to appear in Physical
Review
Tipping time of a quantum rod
The behaviour of a quantum rod, pivoted at its lower end on an impenetrable
floor and restricted to moving in the vertical plane under the gravitational
potential is studied analytically under the approximation that the rod is
initially localised to a small-enough neighbourhood around the point of
classical unstable equilibrium. It is shown that the rod evolves out of this
neighbourhood. The time required for this to happen, i.e., the tipping time is
calculated using the semi-classical path integral. It is shown that equilibrium
is recovered in the classical limit, and that our calculations are consistent
with the uncertainty principle.Comment: 10 pages, 1 figure, To appear in Euro. J. Phy
How well do we know the neutron structure function?
We present a detailed analysis of the uncertainty in the neutron F2n
structure function extracted from inclusive deuteron and proton deep-inelastic
scattering data. The analysis includes experimental uncertainties as well as
uncertainties associated with the deuteron wave function, nuclear smearing, and
nucleon off-shell corrections. Consistently accounting for the Q^2 dependence
of the data and calculations, and restricting the nuclear corrections to
microscopic models of the deuteron, we find significantly smaller uncertainty
in the extracted F2n/F2p ratio than in previous analyses. In addition to
yielding an improved extraction of the neutron structure function, this
analysis also provides an important baseline that will allow future,
model-independent extractions of neutron structure to be used to examine
nuclear medium effects in the the deuteron.Comment: 5 pages, 6 figure
Ideal Linear Chain Polymers with Fixed Angular Momentum
The statistical mechanics of a linear non-interacting polymer chain with a
large number of monomers is considered with fixed angular momentum. The radius
of gyration for a linear polymer is derived exactly by functional integration.
This result is then compared to simulations done with a large number of
non-interacting rigid links at fixed angular momentum. The simulation agrees
with the theory up to finite size corrections. The simulations are also used to
investigate the anisotropic nature of a spinning polymer. We find universal
scaling of the polymer size along the direction of the angular momentum, as a
function of rescaled angular momentum.Comment: 7 pages, 3 figure
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