149 research outputs found
Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath
We derive a Lindblad master equation that approximates the dynamics of a
Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying
the time evolution of operators under the adjoint master equation we prove
that, for large system sizes, these operators attain their thermal equilibrium
expectation values in the long-time limit, and we calculate the rate at which
these values are approached. Integrability of the LMG model prevents
thermalization in the absence of a bath, and our work provides an explicit
proof that the bath indeed restores thermalization. Imposing thermalization on
this otherwise non-thermalizing model outlines an avenue towards probing the
unconventional thermodynamic properties predicted to occur in
ultracold-atom-based realizations of the LMG model.Comment: 10 pages, 3 figure
Eigenvalue distributions from a star product approach
We use the well-known isomorphism between operator algebras and function
spaces equipped with a star product to study the asymptotic properties of
certain matrix sequences in which the matrix dimension tends to infinity.
Our approach is based on the coherent states which allow for a
systematic 1/D expansion of the star product. This produces a trace formula for
functions of the matrix sequence elements in the large- limit which includes
higher order (finite-) corrections. From this a variety of analytic results
pertaining to the asymptotic properties of the density of states, eigenstates
and expectation values associated with the matrix sequence follows. It is shown
how new and existing results in the settings of collective spin systems and
orthogonal polynomial sequences can be readily obtained as special cases. In
particular, this approach allows for the calculation of higher order
corrections to the zero distributions of a large class of orthogonal
polynomials.Comment: 25 pages, 8 figure
Scattering in three-dimensional fuzzy space
We develop scattering theory in a non-commutative space defined by a
coordinate algebra. By introducing a positive operator valued measure as a
replacement for strong position measurements, we are able to derive explicit
expressions for the probability current, differential and total cross-sections.
We show that at low incident energies the kinematics of these expressions is
identical to that of commutative scattering theory. The consequences of spacial
non-commutativity are found to be more pronounced at the dynamical level where,
even at low incident energies, the phase shifts of the partial waves can
deviate strongly from commutative results. This is demonstrated for scattering
from a spherical well. The impact of non-commutativity on the well's spectrum
and on the properties of its bound and scattering states are considered in
detail. It is found that for sufficiently large well-depths the potential
effectively becomes repulsive and that the cross-section tends towards that of
hard sphere scattering. This can occur even at low incident energies when the
particle's wave-length inside the well becomes comparable to the
non-commutative length-scale.Comment: 12 pages, 6 figure
Nutritional management of encapsulating peritoneal sclerosis with intradialytic parenteral nutrition
No Abstract
Spectrum of the three dimensional fuzzy well
We develop the formalism of quantum mechanics on three dimensional fuzzy
space and solve the Schr\"odinger equation for a free particle, finite and
infinite fuzzy wells. We show that all results reduce to the appropriate
commutative limits. A high energy cut-off is found for the free particle
spectrum, which also results in the modification of the high energy dispersion
relation. An ultra-violet/infra-red duality is manifest in the free particle
spectrum. The finite well also has an upper bound on the possible energy
eigenvalues. The phase shifts due to scattering around the finite fuzzy
potential well have been calculated
Duality constructions from quantum state manifolds
The formalism of quantum state space geometry on manifolds of generalised
coherent states is proposed as a natural setting for the construction of
geometric dual descriptions of non-relativistic quantum systems. These state
manifolds are equipped with natural Riemannian and symplectic structures
derived from the Hilbert space inner product. This approach allows for the
systematic construction of geometries which reflect the dynamical symmetries of
the quantum system under consideration. We analyse here in detail the two
dimensional case and demonstrate how existing results in the AdS_2/CFT_1
context can be understood within this framework. We show how the radial/bulk
coordinate emerges as an energy scale associated with a regularisation
procedure and find that, under quite general conditions, these state manifolds
are asymptotically anti-de Sitter solutions of a class of classical dilaton
gravity models. For the model of conformal quantum mechanics proposed by de
Alfaro et. al. the corresponding state manifold is seen to be exactly AdS_2
with a scalar curvature determined by the representation of the symmetry
algebra. It is also shown that the dilaton field itself is given by the quantum
mechanical expectation values of the dynamical symmetry generators and as a
result exhibits dynamics equivalent to that of a conformal mechanical system.Comment: 25 Pages, References Adde
Pharmacotherapy during pregnancy, childbirth and lactation: points and principles to consider (a 2015 update)
Pregnancy, childbirth and lactation pose unique challenges in terms of drug therapy. The pregnant mother and her unborn child are exceptionally vulnerable from a physiological, clinical and ethical standpoint. This warrants careful consideration with respect to a number of important aspects, which could firstly influence the decision to opt for drug therapy, and secondly, could influence the specific agent selected for each indication. The US Food and Drug Administration has introduced changes to the content and format of information presented in prescription drug labelling to assist healthcare providers when assessing benefit versus risk, and in the subsequent counselling of pregnant woman and nursing mothers who need to take medication. This change came into effect at the end of June 2015. This article provides an overview of these important aspects.Keywords: embryo, foetus, lactation, neonate, pregnanc
The entropy of dense non-commutative fermion gases
We investigate the properties of two- and three-dimensional non-commutative
fermion gases with fixed total z-component of angular momentum, J_z, and at
high density for the simplest form of non-commutativity involving constant
spatial commutators. Analytic expressions for the entropy and pressure are
found. The entropy exhibits non-extensive behaviour while the pressure reveals
the presence of incompressibility in two, but not in three dimensions.
Remarkably, for two-dimensional systems close to the incompressible density,
the entropy is proportional to the square root of the system size, i.e., for
such systems the number of microscopic degrees of freedom is determined by the
circumference, rather than the area (size) of the system. The absence of
incompressibility in three dimensions, and subsequently also the absence of a
scaling law for the entropy analogous to the one found in two dimensions, is
attributed to the form of the non-commutativity used here, the breaking of the
rotational symmetry it implies and the subsequent constraint on J_z, rather
than the angular momentum J. Restoring the rotational symmetry while
constraining the total angular momentum J seems to be crucial for
incompressibility in three dimensions. We briefly discuss ways in which this
may be done and point out possible obstacles.Comment: 15 pages, 10 figure
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