2,427,498 research outputs found
The multi-configurational time-dependent Hartree method for bosons: Many-body dynamics of bosonic systems
The evolution of Bose-Einstein condensates is amply described by the
time-dependent Gross-Pitaevskii mean-field theory which assumes all bosons to
reside in a single time-dependent one-particle state throughout the propagation
process. In this work, we go beyond mean-field and develop an essentially-exact
many-body theory for the propagation of the time-dependent Schr\"odinger
equation of interacting identical bosons. In our theory, the time-dependent
many-boson wavefunction is written as a sum of permanents assembled from
orthogonal one-particle functions, or orbitals, where {\it both} the expansion
coefficients {\it and} the permanents (orbitals) themselves are {\it
time-dependent} and fully determined according to a standard time-dependent
variational principle. By employing either the usual Lagrangian formulation or
the Dirac-Frenkel variational principle we arrive at two sets of coupled
equations-of-motion, one for the orbitals and one for the expansion
coefficients. The first set comprises of first-order differential equations in
time and non-linear integro-differential equations in position space, whereas
the second set consists of first-order differential equations with
time-dependent coefficients. We call our theory multi-configurational
time-dependent Hartree for bosons, or MCTDHB(), where specifies the
number of time-dependent orbitals used to construct the permanents. Numerical
implementation of the theory is reported and illustrative numerical examples of
many-body dynamics of trapped Bose-Einstein condensates are provided and
discussed.Comment: 30 pages, 2 figure
Kripke Semantics for Martin-L\"of's Extensional Type Theory
It is well-known that simple type theory is complete with respect to
non-standard set-valued models. Completeness for standard models only holds
with respect to certain extended classes of models, e.g., the class of
cartesian closed categories. Similarly, dependent type theory is complete for
locally cartesian closed categories. However, it is usually difficult to
establish the coherence of interpretations of dependent type theory, i.e., to
show that the interpretations of equal expressions are indeed equal. Several
classes of models have been used to remedy this problem. We contribute to this
investigation by giving a semantics that is standard, coherent, and
sufficiently general for completeness while remaining relatively easy to
compute with. Our models interpret types of Martin-L\"of's extensional
dependent type theory as sets indexed over posets or, equivalently, as
fibrations over posets. This semantics can be seen as a generalization to
dependent type theory of the interpretation of intuitionistic first-order logic
in Kripke models. This yields a simple coherent model theory, with respect to
which simple and dependent type theory are sound and complete
Lie families: theory and applications
We analyze families of non-autonomous systems of first-order ordinary
differential equations admitting a common time-dependent superposition rule,
i.e., a time-dependent map expressing any solution of each of these systems in
terms of a generic set of particular solutions of the system and some
constants. We next study relations of these families, called Lie families, with
the theory of Lie and quasi-Lie systems and apply our theory to provide common
time-dependent superposition rules for certain Lie families.Comment: 23 pages, revised version to appear in J. Phys. A: Math. Theo
Double Relaxation via AdS/CFT
We exploit the AdS/CFT correspondence to investigate thermalization in an N=2
strongly coupled gauge theory including massless fundamental matter (quark).
More precisely, we consider the response of a zero temperature state of the
gauge theory under variation of an external electric field leading to a
time-dependent current. The holographic dual of the above set-up is given by
introducing a time-dependent electric field on the probe D7-brane embedded in
an AdS_5 X S^5 background. In the dual gravity theory, due to a time-dependent
electric field an apparent horizon forms on the brane which, according to
AdS/CFT dictionary, is the counterpart of the thermalization process in the
gauge theory. We classify different functions for time-dependent electric field
and study their effect on the apparent horizon formation. In the case of pulse
functions where the electric field varies from zero to zero, apart from
non-equilibrium phase, we observe that two apparent horizons form on the brane.
On the gauge theory side, it means that the state of the gauge theory
experiences two different temperatures during the time evolution.Comment: 28 pages, 13 figures, published versio
A local-global principle for linear dependence of noncommutative polynomials
A set of polynomials in noncommuting variables is called locally linearly
dependent if their evaluations at tuples of matrices are always linearly
dependent. By a theorem of Camino, Helton, Skelton and Ye, a finite locally
linearly dependent set of polynomials is linearly dependent. In this short note
an alternative proof based on the theory of polynomial identities is given. The
method of the proof yields generalizations to directional local linear
dependence and evaluations in general algebras over fields of arbitrary
characteristic. A main feature of the proof is that it makes it possible to
deduce bounds on the size of the matrices where the (directional) local linear
dependence needs to be tested in order to establish linear dependence.Comment: 8 page
Classical Scattering in Dimensional String Theory
We find the general solution to Polchinski's classical scattering equations
for dimensional string theory. This allows efficient computation of
scattering amplitudes in the standard Liouville background.
Moreover, the solution leads to a mapping from a large class of time-dependent
collective field theory backgrounds to corresponding nonlinear sigma models.
Finally, we derive recursion relations between tachyon amplitudes. These may be
summarized by an infinite set of nonlinear PDE's for the partition function in
an arbitrary time-dependent background.Comment: 15 p
A Theory of Bayesian Decision Making
This paper presents a complete, choice-based, axiomatic Bayesian decision theory. It introduces a new choice set consisting of information-contingent plans for choosing actions and bets and subjective expected utility model with effect-dependent utility functions and action-dependent subjective probabilities which, in conjunction with the updating of the probabilities using Bayes' rule, gives rise to a unique prior and a set of action-dependent posterior probabilities representing the decision maker's prior and posterior beliefs.
Large amplitude collective dynamic beyond the independent particle/quasiparticle picture
In the present note, a summary of selected aspects of time-dependent
mean-field theory is first recalled. This approach is optimized to describe
one-body degrees of freedom. A special focus is made on how this microscopic
theory can be reduced to a macroscopic dynamic for a selected set of collective
variables. Important physical phenomena like adiabaticity/diabaticity, one-body
dissipation or memory effect are discussed. Special aspects related to the use
of a time-dependent density functional instead of a time-dependent Hartree-Fock
theory based on a bare hamiltonian are underlined. The absence of proper
description of complex internal correlations however strongly impacts the
predictive power of mean-field. A brief overview of theories going beyond the
independent particles/quasi-particles theory is given. Then, a special
attention is paid for finite fermionic systems at low internal excitation. In
that case, quantum fluctuations in collective space that are poorly treated at
the mean-field level, are important. Several approaches going beyond
mean-field, that are anticipated to improve the description of quantum
fluctuations, are discussed: the Balian-V\'en\'eroni variational principle, the
Time-Dependent Random Phase Approximation and the recently proposed Stochastic
Mean-Field theory. Relations between these theories are underlined as well as
their advantages and shortcomings.Comment: To be published in the ebook "Progress of time-dependent nuclear
reaction theory" honoring Prof. Joachim Maruhn's retiremen
Effective field theory interpretation of searches for dark matter annihilation in the Sun with the IceCube Neutrino Observatory
We present a model-independent interpretation of searches for dark matter
annihilation in the Sun using an effective field theory approach. We identify a
set of effective operators contributing to spin-dependent scattering of dark
matter with protons in the non-relativistic limit and explore simple new
physics models which would give rise to such operators. Using the limits on the
spin-dependent scattering cross-section set by the IceCube collaboration in
their search for dark matter annihilation in the Sun, we derive limits on
effective couplings and corresponding masses of mediating particles. We show
that the effective field theory interpretation of the IceCube searches provides
constraints on dark matter complementary to those from relic density
observations and searches at the LHC. Finally, we discuss the impact of
astrophysical uncertainties on our results.Comment: 16 pages, 6 figures; Added references in v
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