604 research outputs found
Quantum Parametric Resonance of a dissipative oscillator: fading and persistent memory in the long-time evolution
The evolution of a quantum oscillator, with periodically varying frequency
and damping, is studied in the two cases of parametric resonance (PR) producing
a limited, or unlimited stretching of the wave function. The different
asymptotic behaviors of the energy distribution, show the non trivial interplay
between PR and the initial quantum state. In the first case, the oscillator's
mean energy tends asymptotically to a fully classical value, independent of the
initial state, with vanishing relative quantum fluctuations. In the second
case, the memory of the initial state persists over arbitrary long time scales,
both in the mean value and in the large quantum fluctuations of the energy.Comment: 20 pages, 2 figure
Bogoliubov theory of interacting bosons: new insights from an old problem
In a gas of interacting bosons, the Hamiltonian , obtained by
dropping all the interaction terms between free bosons with moment
, is diagonalized exactly. The resulting
eigenstates depend on two discrete indices
, where numerates the \emph{quasiphonons}
carrying a moment , responsible for transport or dissipation
processes. , in turn, numerates a ladder of \textquoteleft
vacua\textquoteright, with increasing
equispaced energies, formed by boson pairs with opposite moment. Passing from
one vacuum to another (), results from
creation/annihilation of new momentless collective excitations, that we call
\emph{vacuons}. Exact quasiphonons originate from one of the vacua by
\textquoteleft creating\textquoterightan asymmetry in the number of
opposite moment bosons. The well known Bogoliubov collective excitations (CEs)
are shown to coincide with the exact eigenstates
, i.e. with the quasiphonons created from
the lowest-level vacuum (). All this is discussed, in view of existing or
future experimental observations of the vacuons (PBs), a sort of bosonic Cooper
pairs, which are the main factor of novelty beyond Bogoliubov theory.Comment: 13 pages, 1 figur
Exact canonic eigenstates of the truncated Bogoliubov Hamiltonian in an interacting bosons gas
In a gas of weakly interacting bosons \cite{Bogo1, Bogo2}, a truncated
canonic Hamiltonian follows from dropping all the interaction
terms between free bosons with momentum .
Bogoliubov Canonic Approximation (BCA) is a further manipulation, replacing the
number \emph{operator} of free particles in
, with the total number of bosons. BCA transforms
into a different Hamiltonian
,
where and create/annihilate non
interacting pseudoparticles. The problem of the \emph{exact} eigenstates of the
truncated Hamiltonian is completely solved in the thermodynamic limit (TL) for
a special class of eigensolutions , denoted as
\textquoteleft s-pseudobosons\textquoteright, with energies
and \emph{zero} total momentum. Some preliminary results
are given for the exact eigenstates (denoted as \textquoteleft
-pseudobosons\textquoteright), carrying a total momentum
(). A comparison is done with
and with the Gross-Pitaevskii theory (GPT), showing that some
differences between exact and BCA/GPT results persist even in the TL. Finally,
it is argued that the emission of -pseudobosons, which is responsible for
the dissipation \emph{la} Landau \cite{L}, could be significantly
different from the usual picture, based on BCA pseudobosons
Gas in external fields: the weird case of the logarithmic trap
The effects of an attractive logarithmic potential on a gas
of non interacting particles (Bosons or Fermions), in a box of volume
, are studied in dimensions. The unconventional behavior of the
gas challenges the current notions of thermodynamic limit and size
independence. When and diverge, with finite density
and finite trap strength , the gas collapses in the ground state,
independently from the bosonic/fermionic nature of the particles, at \emph{any}
temperature. If, instead, , there exists a critical
temperature , such that the gas remains in the ground state at any
, and "evaporates" above, in a non-equilibrium state of borderless
diffusion. For the gas to exhibit a conventional Bose-Einstein condensation
(BEC) or a finite Fermi level, the strength must vanish with
, according to a complicated exponential relationship, as
a consequence of the exponentially increasing density of states, specific of
the logarithmic trap.Comment: 21 pages, 3 figure
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