6,725 research outputs found
Entropy and Temperature of a Quantum Carnot Engine
It is possible to extract work from a quantum-mechanical system whose
dynamics is governed by a time-dependent cyclic Hamiltonian. An energy bath is
required to operate such a quantum engine in place of the heat bath used to run
a conventional classical thermodynamic heat engine. The effect of the energy
bath is to maintain the expectation value of the system Hamiltonian during an
isoenergetic expansion. It is shown that the existence of such a bath leads to
equilibrium quantum states that maximise the von Neumann entropy. Quantum
analogues of certain thermodynamic relations are obtained that allow one to
define the temperature of the energy bath.Comment: 4 pages, 1 figur
Unusual quantum states: nonlocality, entropy, Maxwell's daemon, and fractals
This paper analyses the mathematical properties of some unusual quantum
states that are constructed by inserting an impenetrable barrier into a chamber
confining a single particle.Comment: 9 Figure
Geometry of PT-symmetric quantum mechanics
Recently, much research has been carried out on Hamiltonians that are not
Hermitian but are symmetric under space-time reflection, that is, Hamiltonians
that exhibit PT symmetry. Investigations of the Sturm-Liouville eigenvalue
problem associated with such Hamiltonians have shown that in many cases the
entire energy spectrum is real and positive and that the eigenfunctions form an
orthogonal and complete basis. Furthermore, the quantum theories determined by
such Hamiltonians have been shown to be consistent in the sense that the
probabilities are positive and the dynamical trajectories are unitary. However,
the geometrical structures that underlie quantum theories formulated in terms
of such Hamiltonians have hitherto not been fully understood. This paper
studies in detail the geometric properties of a Hilbert space endowed with a
parity structure and analyses the characteristics of a PT-symmetric Hamiltonian
and its eigenstates. A canonical relationship between a PT-symmetric operator
and a Hermitian operator is established. It is shown that the quadratic form
corresponding to the parity operator, in particular, gives rise to a natural
partition of the Hilbert space into two halves corresponding to states having
positive and negative PT norm. The indefiniteness of the norm can be
circumvented by introducing a symmetry operator C that defines a positive
definite inner product by means of a CPT conjugation operation.Comment: 22 Page
Faster than Hermitian Quantum Mechanics
Given an initial quantum state |psi_I> and a final quantum state |psi_F> in a
Hilbert space, there exist Hamiltonians H under which |psi_I> evolves into
|psi_F>. Consider the following quantum brachistochrone problem: Subject to the
constraint that the difference between the largest and smallest eigenvalues of
H is held fixed, which H achieves this transformation in the least time tau?
For Hermitian Hamiltonians tau has a nonzero lower bound. However, among
non-Hermitian PT-symmetric Hamiltonians satisfying the same energy constraint,
tau can be made arbitrarily small without violating the time-energy uncertainty
principle. This is because for such Hamiltonians the path from |psi_I> to
|psi_F> can be made short. The mechanism described here is similar to that in
general relativity in which the distance between two space-time points can be
made small if they are connected by a wormhole. This result may have
applications in quantum computing.Comment: 4 page
Deconvolution for an atomic distribution: rates of convergence
Let be i.i.d.\ copies of a random variable where and and are independent and have the same
distribution as and respectively. Assume that the random variables
's are unobservable and that where and are independent,
has a Bernoulli distribution with probability of success equal to and
has a distribution function with density Let the random variable
have a known distribution with density Based on a sample
we consider the problem of nonparametric estimation of the
density and the probability Our estimators of and are
constructed via Fourier inversion and kernel smoothing. We derive their
convergence rates over suitable functional classes. By establishing in a number
of cases the lower bounds for estimation of and we show that our
estimators are rate-optimal in these cases.Comment: 27 page
Wide band frequency tracker performance and design of an all angle laser Doppler optical homodyne receiver, ground wind and wind tunnel measurements program, volume 2 Final report
Analysis and measurement of characteristics of wide band frequency trackers and design and fabrication of all angle laser Doppler velocimete
- …