Papers available online

Fokker-Planck equations for eigenstate distributions
Letters in Mathematical Physics 25, 161-174 (1992)

A simple model of relaxation phenomena is defined with a variable strength
of interaction and where the interaction term is given by a Gaussian
unitary ensemble of random matrices. A set of Fokker-Planck equations are
derived which describe the gradual delocalization with increasing strength
of interaction of the eigenstates with respect to the unperturbed energy
eigenbasis. The effect of localization on the time evolution is a
nonergodic property: the system has a memory of  the initial state.
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Determinism and randomness in quantum dynamics 
Journal of Physics A 26, 7193-7211 (1993)

A class of models is considered where a finite or infinite quantum
dynamical system in a stationary state is probed by sequences of
observations acting on a specified finite subsystem. The whole set of such
experiments is described by a time-ordered (causal) and stationary quantum
correlation kernel. It is shown that any such kernel can be decomposed in
a unique way into a convex combination of two kernels, here called the
regular and singular components. A singular system has a strong
deterministic property, the predictability of the future from the
knowledge of the past is limited only by the inevitable indeterminism of
quantum measurements. Furthermore, in this case the full set of
correlation functions of arbitrary time order, and hence the dynamical
system itself,  is determined by the causal kernel. Finite systems and
infinite systems satisfying the KMS condition at finite temperature are of
this type. In the regular case the dynamics  contains a shift, there is a
genuine asymptotic randomness and the dynamical system cannot be
reconstructed in a unique way from the causal kernel. Nontrivial quantum
Markov processes are shown to belong to this class.
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Irreversibility and randomness in linear response theory
Journal of Statistical Physics 72, 539-554 (1993)

Recall that the fluctuation-dissipation theorem connects the response
function of a passive linear system and the spectral density of the
stationary stochastic process which describes the thermal fluctuations in
the system. It is shown that the classical limit \hbar = 0 of the
fluctuation dissipation theorem implies a correspondence between systems
which are reversible in the sense that the energy used to drive it away
from equilibrium is completely recoverable as work and processes which are
deterministic in the sense of Wiener's prediction theory, while
irreversible systems correspond to non-deterministic processes. This
correspondence is expressed by a simple transformation between the
operator kernel which determines the optimal choice of the time-dependent
force and the linear predictor for the stochastic process. For quantum
systems this correspondence does not hold, the fluctuations are always of
the deterministic type for any finite temperature, but the system is not
necessarily reversible. For irreversible systems a formula is derived for
the instantaneous entropy production which is a generalization of the
standard one for Markovian dynamics.
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Decoherence properties of finite quantum systems
1993, unpublished

In this paper some of the properties of the correlation functions for
finite quantum systems (with  unitary dynamics and discrete spectra)  are
investigated using methods from operator algebras and quantum statistical
mechanics. Their information content and  decoherence properties are
measured by entropy functionals in a formalism which is capable of dealing
with approximate measurements as well as the ideal ones defined by
orthogonal projectors. Necessary and sufficient decoherence conditions are
found for the observables to form a classical commutative system. These
conditions  involve the correlation functions of all orders, and the
systems satisfying them exactly are exceptional. On the other hand it is
shown that for large but finite quantum systems most observables will
approximately satisfy a chaotic form of decoherence condition for
correlation functions of not too high order. It is also possible to choose
observables which define nearly deterministic (and hence decoherent)
histories over a finite time.
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On the existence of quantum subdynamics
Journal of Physics A 29, 4197-4207 (1996)

It is shown, using only elementary operator algebra, that an open quantum
system coupled to its environment will have a subdynamics (reduced
dynamics) as an exact consequence of the reversible dynamics of the
composite system only when the states of system and environment are
uncorrelated.  Furthermore, it is proved that for a finite temperature the
KMS condition for the lowest order correlation function cannot be
reproduced by any type of linear subdynamics except the reversible
Hamiltonian one of a closed system.  The first statement can be seen as a
particular case of a much more general theorem of Takesaki on the
properties of conditional expectations in von Neumann algebras.  The
concept of subdynamics used here allows for memory effects, no assumption
is made of a Markov property.  For dynamical systems based on commutative
algebras of observables the subdynamics always exists as a stochastic
process in the random variable defining the open subsystem.
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Brownian motion of quantum harmonic oscillators: existence of a subdynamics
Journal of Mathematical Physics 39(5), 2763-80 (1998)

The effects of system-environment correlations on the dynamics of an 
open quantum system are investigated for the standard model of a set 
of quantum harmonic oscillators interacting with a heat bath of 
oscillators.  The observable properties of the open system are 
completely defined by a matrix-valued covariance function, this fact 
allows a simple but detailed analysis.  There is a subdynamics when 
this function comes from transformations of the open system 
observables alone.  We show that this happens only when the states of 
system and environment are uncorrelated, while for classical systems 
there is always a subdynamics.  A quantum subdynamics cannot have the 
properties we associate with thermal fluctuations, the KMS relation 
for the covariance function at a finite temperature implies that the 
system must be closed.  The conditions for having a subdynamics as a 
good approximation to the exact closed dynamics are investigated, and 
so are the similar but stronger conditions for a Markovian dynamics.  
It is also shown how a subdynamics defines the response of the open 
system to some types of time dependent external forces.
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A general no-cloning theorem
Letters in Mathematical Physics 47(2), 189-196 (1999)

A simple theorem is proved which has most of the known no-cloning  and
no-broadcasting results as corollaries. It also implies the  standard
restrictions on measuring  non-commuting observables.
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Cloning the quantum oscillator