341 research outputs found
PT-symmetric deformations of integrable models
We review recent results on new physical models constructed as PT-symmetrical
deformations or extensions of different types of integrable models. We present
non-Hermitian versions of quantum spin chains, multi-particle systems of
Calogero-Moser-Sutherland type and non-linear integrable field equations of
Korteweg-de-Vries type. The quantum spin chain discussed is related to the
first example in the series of the non-unitary models of minimal conformal
field theories. For the Calogero-Moser-Sutherland models we provide three
alternative deformations: A complex extension for models related to all types
of Coxeter/Weyl groups; models describing the evolution of poles in constrained
real valued field equations of non linear integrable systems and genuine
deformations based on antilinearly invariant deformed root systems.
Deformations of complex nonlinear integrable field equations of KdV-type are
studied with regard to different kinds of PT-symmetrical scenarios. A reduction
to simple complex quantum mechanical models currently under discussion is
presented.Comment: 21 pages, 3 figure
Weak values of electron spin in a double quantum dot
We propose a protocol for a controlled experiment to measure a weak value of
the electron's spin in a solid state device. The weak value is obtained by a
two step procedure -- weak measurement followed by a strong one
(post-selection), where the outcome of the first measurement is kept provided a
second post-selected outcome occurs. The set-up consists of a double quantum
dot and a weakly coupled quantum point contact to be used as a detector.
Anomalously large values of the spin of a two electron system are predicted, as
well as negative values of the total spin. We also show how to incorporate the
adverse effect of decoherence into this procedure.Comment: 4+ pages, 3 figures, final published versio
Tomography of many-body weak values: Mach-Zehnder interferometry
We propose and study a weak value (WV) protocol in the context of a solid
state setup, specifically, an electronic Mach-Zehnder interferometer. This is
the first specific proposal to measure both the real and imaginary part (i.e.,
complete tomography) of a WV. We also analyze the manifestation of many-body
physics in the WV to be measured, including finite temperature and
shot-noise-like contributions.Comment: 4+ pages, 2 figure
Non-gaussianities and the Stimulated creation of quanta in the inflationary universe
Cosmological inflation generates a spectrum of density perturbations that can
seed the cosmic structures we observe today. These perturbations are usually
computed as the result of the gravitationally-induced spontaneous creation of
perturbations from an initial vacuum state. In this paper, we compute the
perturbations arising from gravitationally-induced stimulated creation when
perturbations are already present in the initial state. The effect of these
initial perturbations is not diluted by inflation and survives to its end, and
beyond. We consider a generic statistical density operator describing an
initial mixed state that includes probabilities for nonzero numbers of scalar
perturbations to be present at early times during inflation. We analyze the
primordial bispectrum for general configurations of the three different
momentum vectors in its arguments. We find that the initial presence of quanta
can significantly enhance non-gaussianities in the so-called squeezed limit.
Our results show that an observation of non-gaussianities in the squeezed limit
can occur for single-field inflation when the state in the very early
inflationary universe is not the vacuum, but instead contains early-time
perturbations. Valuable information about the initial state can then be
obtained from observations of those non-gaussianities.Comment: 25 page
Anyons in 1+1 Dimensions
The possibility of excitations with fractional spin and statististics in
dimensions is explored. The configuration space of a two-particle system
is the half-line. This makes the Hamiltonian self-adjoint for a family of
boundary conditions parametrized by one real number . The limit ) reproduces the propagator of non-relativistic
particles whose wavefunctions are even (odd) under particle exchange. A
relativistic ansatz is also proposed which reproduces the correct Polyakov spin
factor for the spinning particle in dimensions. These checks support
validity of the interpretation of as a parameter related to the
``spin'' that interpolates continuously between bosons () and
fermions (). Our approach can thus be useful for obtaining the
propagator for one-dimensional anyons.Comment: 13p. latex (Revtex), no figures
Mixed-state twin observables
Twin observables, i.e. opposite subsystem observables A+ and A- that are
indistinguishable in measurement in a given mixed or pure state W, are
investigated in detail algebraicly and geometrically. It is shown that there is
a far-reaching correspondence between the detectable (in W) spectral entities
of the two operators. Twin observables are state-dependently quantum-logically
equivalent, and direct subsystem measurement of one of them ipso facto gives
rise to the indirect (i.e. distant) measurement of the other. Existence of
nontrivial twins requires singularity of W. Systems in thermodynamic
equilibrium do not admit subsystem twins. These observables may enable one to
simplify the matrix representing W.Comment: 13 page
A spin chain model with non-Hermitian interaction: the Ising quantum spin chain in an imaginary field
We investigate a lattice version of the Yang-Lee model which is characterized by a non-Hermitian quantum spin chain Hamiltonian. We propose a new way to implement PT-symmetry on the lattice, which serves to guarantee the reality of the spectrum in certain regions of values of the coupling constants. In that region of unbroken PT-symmetry we construct a Dyson map, a metric operator and find the Hermitian counterpart of the Hamiltonian for small values of the number of sites, both exactly and perturbatively. Besides the standard perturbation theory about the Hermitian part of the Hamiltonian, we also carry out an expansion in the second coupling constant of the model. Our constructions turns out to be unique with the sole assumption that the Dyson map is Hermitian. Finally we compute the magnetization of the chain in the z and x direction
Quantum state discrimination: a geometric approach
We analyse the problem of finding sets of quantum states that can be
deterministically discriminated. From a geometric point of view this problem is
equivalent to that of embedding a simplex of points whose distances are maximal
with respect to the Bures distance (or trace distance). We derive upper and
lower bounds for the trace distance and for the fidelity between two quantum
states, which imply bounds for the Bures distance between the unitary orbits of
both states. We thus show that when analysing minimal and maximal distances
between states of fixed spectra it is sufficient to consider diagonal states
only. Hence considering optimal discrimination, given freedom up to unitary
orbits, it is sufficient to consider diagonal states. This is illustrated
geometrically in terms of Weyl chambers.Comment: 12 pages, 2 figure
Enhanced local-type inflationary trispectrum from a non-vacuum initial state
We compute the primordial trispectrum for curvature perturbations produced
during cosmic inflation in models with standard kinetic terms, when the initial
quantum state is not necessarily the vacuum state. The presence of initial
perturbations enhances the trispectrum amplitude for configuration in which one
of the momenta, say , is much smaller than the others, . For those squeezed configurations the trispectrum acquires the
so-called local form, with a scale dependent amplitude that can get values of
order . This amplitude can be larger than the
prediction of the so-called Maldacena consistency relation by a factor ,
and can reach the sensitivity of forthcoming observations, even for
single-field inflationary models.Comment: 11 pages, 1 figure. References added, typos corrected, minor change
Generalised Player Modelling : Why Artificial Intelligence in Games Should Incorporate Meaning, with a Formalism for so Doing
General game-playing artificial intelligence (AI) has recently seen important advances due to the various techniques known as ‘deep learning’. However, in terms of human-computer interaction, the advances conceal a major limitation: these algorithms do not incorporate any sense of what human players find meaningful in games. I argue that adaptive game AI will be enhanced by a generalised player model, because games are inherently human artefacts which require some encoding of the human perspective in order to respond naturally to individual players. The player model provides constraints on the adaptive AI, which allow it to encode aspects of what human players find meaningful. I propose that a general player model requires parameters for the subjective experience of play, including: player psychology, game structure, and actions of play. I argue that such a player model would enhance efficiency of per-game solutions, and also support study of game-playing by allowing (within-player) comparison between games, or (within-game) comparison between players (human and AI). Here we detail requirements for functional adaptive AI, arguing from first-principles drawn from games research literature, and propose a formal specification for a generalised player model based on our ‘Behavlets’ method for psychologically-derived player modelling.Peer reviewe
- …