1,110 research outputs found
Microcanonical Entropy and Dynamical Measure of Temperature for Systems with Two First Integrals
We consider a generic classical many particle system described by an
autonomous Hamiltonian which, in addition, has a
conserved quantity , so that the Poisson bracket
vanishes. We derive in detail the microcanonical expressions for
entropy and temperature. We show that both of these quantities depend on
multidimensional integrals over submanifolds given by the intersection of the
constant energy hypersurfaces with those defined by
. We show that temperature and higher order
derivatives of entropy are microcanonical observable that, under the hypothesis
of ergodicity, can be calculated as time averages of suitable functions. We
derive the explicit expression of the function that gives the temperature.Comment: 4 pages, preprin
Microcanonical entropy for classical systems
The entropy definition in the microcanonical ensemble is revisited. We
propose a novel definition for the microcanonical entropy that resolve the
debate on the correct definition of the microcanonical entropy. In particular
we show that this entropy definition fixes the problem inherent the exact
extensivity of the caloric equation. Furthermore, this entropy reproduces
results which are in agreement with the ones predicted with standard Boltzmann
entropy when applied to macroscopic systems. On the contrary, the predictions
obtained with the standard Boltzmann entropy and with the entropy we propose,
are different for small system sizes. Thus, we conclude that the Boltzmann
entropy provides a correct description for macroscopic systems whereas
extremely small systems should be better described with the entropy that we
propose here.Comment: 5 pages, 2 figure
Entanglement estimation in non-optimal qubit states
In the last years, a relationship has been established between the quantum
Fisher information (QFI) and quantum entanglement. In the case of two-qubit
systems, all pure entangled states can be made useful for sub-shot-noise
interferometry while their QFI meets a necessary and sufficient condition [1].
In M-qubit systems, the QFI provides just a sufficient condition in the task of
detecting the degree of entanglement of a generic state [2]. In our work, we
show analytically that, for a large class of one-parameter non-optimal
two-qubit states, the maximally entangled states are associated with stationary
points of the QFI, as a function of such parameter. We show, via numerical
simulations, that this scenario is maintained for the generalisation of this
class of states to a generic M-qubit system. Furthermore, we suggest a scheme
for an interferometer able to detect the entanglement in a large class of
two-spin states.Comment: 7 pages, 7 figure
Topology and Phase Transitions II. Theorem on a necessary relation
In this second paper, we prove a necessity Theorem about the topological
origin of phase transitions. We consider physical systems described by smooth
microscopic interaction potentials V_N(q), among N degrees of freedom, and the
associated family of configuration space submanifolds {M_v}_{v \in R}, with
M_v={q \in R^N | V_N(q) \leq v}. On the basis of an analytic relationship
between a suitably weighed sum of the Morse indexes of the manifolds {M_ v}_{v
\in R} and thermodynamic entropy, the Theorem states that any possible unbound
growth with N of one of the following derivatives of the configurational
entropy S^{(-)}(v)=(1/N) \log \int_{M_v} d^Nq, that is of |\partial^k
S^{(-)}(v)/\partial v^k|, for k=3,4, can be entailed only by the weighed sum of
Morse indexes.
Since the unbound growth with N of one of these derivatives corresponds to
the occurrence of a first or of a second order phase transition, and since the
variation of the Morse indexes of a manifold is in one-to-one correspondence
with a change of its topology, the Main Theorem of the present paper states
that a phase transition necessarily stems from a topological transition in
configuration space. The proof of the Theorem given in the present paper cannot
be done without Main Theorem of paper I.Comment: 21 pages. This second paper follows up paper I archived in
math-ph/0505057. Added minor changes: Title, Abstract, Introductio
Probing EWSB through vector boson scattering at the LHC
We estimate the power of the LHC in probing effects of strongly-interacting
symmetry breaking sector through vector boson scattering in a complete partonic
analysis.Comment: Talk given at IFAE 2009, Bari, Italy, 15-17 April 200
Newton's cradle analogue with Bose-Einstein condensates
We propose a possible experimental realization of a quantum analogue of
Newton's cradle using a configuration which starts from a Bose-Einstein
condensate. The system consists of atoms with two internal states trapped in a
one dimensional tube with a longitudinal optical lattice and maintained in a
strong Tonks-Girardeau regime at maximal filling. In each site the wave
function is a superposition of the two atomic states and a disturbance of the
wave function propagates along the chain in analogy with the propagation of
momentum in the classical Newton's cradle. The quantum travelling signal is
generally deteriorated by dispersion, which is large for a uniform chain and is
known to be zero for a suitably engineered chain, but the latter is hardly
realizable in practice. Starting from these opposite situations we show how the
coherent behaviour can be enhanced with minimal experimental effort.Comment: To appear in Journal of Physics
Nonclassical dynamics of Bose condensates in an optical lattice in the superfluid regime
A condensate in an optical lattice, prepared in the ground state of the
superfluid regime, is stimulated first by suddenly increasing the optical
lattice amplitude and then, after a waiting time, by abruptly decreasing this
amplitude to its initial value. Thus the system is first taken to the Mott
regime and then back to the initial superfluid regime. We show that, as a
consequence of this nonadiabatic process, the system falls into a configuration
far from equilibrium whose superfluid order parameter is described in terms of
a particular superposition of Glauber coherent states that we derive. We also
show that the classical equations of motion describing the time evolution of
this system are inequivalent to the standard discrete nonlinear Schreodinger
equations. By numerically integrating such equations with several initial
conditions, we show that the system loses coherence, becoming insulating.Comment: 5 pages, 4 figure
Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
We consider a family of chaotic Bose-Hubbard Hamiltonians (BHH) parameterized
by the coupling strength between neighboring sites. As increases the
eigenstates undergo changes, reflected in the structure of the Local Density of
States. We analyze these changes, both numerically and analytically, using
perturbative and semiclassical methods. Although our focus is on the quantum
trimer, the presented methodology is applicable for the analysis of longer
lattices as well.Comment: 4 pages, 4 figure
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