927 research outputs found

### Fock representation of the renormalized higher powers of white noise and the Virasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra

The identification of the $*$--Lie algebra of the renormalized higher powers
of white noise (RHPWN) and the analytic continuation of the second quantized
Virasoro--Zamolodchikov--$w_{\infty} *$--Lie algebra of conformal field theory
and high-energy physics, was recently established in \cite{id} based on results
obtained in [1] and [2]. In the present paper we show how the RHPWN Fock
kernels must be truncated in order to be positive definite and we obtain a Fock
representation of the two algebras. We show that the truncated renormalized
higher powers of white noise (TRHPWN) Fock spaces of order $\geq 2$ host the
continuous binomial and beta processes

### Quantum stochastic equation for test particle interacting with dilute Bose gas

We use the stochastic limit method to study long time quantum dynamics of a
test particle interacting with a dilute Bose gas. The case of arbitrary
form-factors and an arbitrary, not necessarily equilibrium, quasifree low
density state of the Bose gas is considered. Starting from microscopic dynamics
we derive in the low density limit a quantum white noise equation for the
evolution operator. This equation is equivalent to a quantum stochastic
equation driven by a quantum Poisson process with intensity $S-1$, where $S$ is
the one-particle $S$ matrix. The novelty of our approach is that the equations
are derived directly in terms of correlators, without use of a Fock-antiFock
(or Gel'fand-Naimark-Segal) representation. Advantages of our approach are the
simplicity of derivation of the limiting equation and that the algebra of the
master fields and the Ito table do not depend on the initial state of the Bose
gas. The notion of a causal state is introduced. We construct master fields
(white noise and number operators) describing the dynamics in the low density
limit and prove the convergence of chronological (causal) correlators of the
field operators to correlators of the master fields in the causal state.Comment: 21 pages, LaTeX, published version (few improvements

### A stochastic golden rule and quantum Langevin equation for the low density limit

A rigorous derivation of quantum Langevin equation from microscopic dynamics
in the low density limit is given. We consider a quantum model of a microscopic
system (test particle) coupled with a reservoir (gas of light Bose particles)
via interaction of scattering type. We formulate a mathematical procedure (the
so-called stochastic golden rule) which allows us to determine the quantum
Langevin equation in the limit of large time and small density of particles of
the reservoir. The quantum Langevin equation describes not only dynamics of the
system but also the reservoir. We show that the generator of the corresponding
master equation has the Lindblad form of most general generators of completely
positive semigroups

### Nuclear physics with a medium-energy Electron-Ion Collider

A polarized ep/eA collider (Electron-Ion Collider, or EIC) with variable
center-of-mass energy sqrt(s) ~ 20-70 GeV and a luminosity ~ 10^{34} cm^{-2}
s^{-1} would be uniquely suited to address several outstanding questions of
Quantum Chromodynamics (QCD) and the microscopic structure of hadrons and
nuclei: (i) the three-dimensional structure of the nucleon in QCD (sea quark
and gluon spatial distributions, orbital motion, polarization, correlations);
(ii) the fundamental color fields in nuclei (nuclear parton densities,
shadowing, coherence effects, color transparency); (iii) the conversion of
color charge to hadrons (fragmentation, parton propagation through matter,
in-medium jets). We briefly review the conceptual aspects of these questions
and the measurements that would address them, emphasizing the qualitatively new
information that could be obtained with the collider. Such a medium-energy EIC
could be realized at Jefferson Lab after the 12 GeV Upgrade (MEIC), or at
Brookhaven National Lab as the low-energy stage of eRHIC.Comment: 9 pages, 5 figures. Mini-review compiled in preparation for the MEIC
Conceptual Design Report, Jefferson Lab (2011

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