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 $\rho$ 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

Nichtigkeit bei der Einberufung der Mitgliederversammlung

v.15:no.3:suppl.(1935:May 15

Anyons in 1+1 Dimensions

The possibility of excitations with fractional spin and statististics in $1+1$ 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 $\gamma$. The limit $\gamma \rightarrow 0, (\infty$) 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 $1+1$ dimensions. These checks support validity of the interpretation of $\gamma$ as a parameter related to the ``spin'' that interpolates continuously between bosons ($\gamma =0$) and fermions ($\gamma =\infty$). 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

Convulsant actions of 4-aminopyridine on the guinea-pig olfactory cortex slice

The effects of bath-applied 4-aminopyridine on neurones and extracellular potassium and calcium concentrations were recorded in slices of guinea-pig olfactory cortex. Neurones were orthodromically activated by stimulating the lateral olfactory tract. 4-Aminopyridine (3–10 μM) had the following effects: (1) an increase in the frequency and amplitude of spontaneous postsynaptic potentials: (2) a prolongation and oscillatory behaviour or orthodromically evoked postsynaptic potentials; (3) induction of spontaneous or stimulus-evoked seizure-type discharges which were accompanied by large rises in extracellular potassium and falls in calcium concentration; (4) a prolongation of the lateral olfactory tract population fibre spike. Prior to paroxysmal depolarization, membrane potential, input resistance and soma spike duration were unaffected. In the seconds before seizure discharges, a late hyperpolarizing potential (evoked by orthodromic stimulation) was reduced in amplitude or abolished. Diphenylhydantoin (50 μM) or magnesium ions (5 mM) prevented paroxysmal activity. Our results whow that 4-aminopyridine can produce seizure-type discharges in a brain slice preparation. The role of increased spontaneous potentials and possible loss of synaptic inhibition as causal factors for such discharges is discussed

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 $k_3$, is much smaller than the others, $k_3 \ll k_{1,2,4}$. For those squeezed configurations the trispectrum acquires the so-called local form, with a scale dependent amplitude that can get values of order $\epsilon ({k_1}/{k_3})^2$. This amplitude can be larger than the prediction of the so-called Maldacena consistency relation by a factor $10^6$, 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