Squeezed states, metaplectic group, and operator möbius transformations

We present an analysis, based on the metaplectic group Mp(2), of the recently introduced single-mode inverse creation and annihilation operators and of the associated eigenstates of different two-photon annihilation operators. We motivate and obtain a quantum operator form of the classical Mobius or fractional linear transformation. The subtle relation to the two unitary irreducible representations of Mp(2) is brought out. For problems involving inverse operators the usefulness of the Bargmann analytic function representation of quantum mechanics is demonstrated. Squeezing, bunching, and photon-number distributions of the four families of states that arise in this context are studied both analytically and numerically

Squeezed vacuum as an eigenstate of two-photon annihilation operator

We introduce the inverse annihilation and creation operators a-1 and a(dagger-1) by their actions on the number states. We show that the squeezed vacuum exp(1/2xia(dagger2)]\0] and squeezed first number state exp[1.2xia(dagger2)]\n = 1] are respectively the eigenstates of the operators (a(dagger-1)a) and (aa(dagger-1)) with the eigenvalue xi.

Symmetry-breaking transition in a two-level system coupled to an Ohmic bath: A squeezed-state approach

Displaced squeezed states are proposed as variational ground states for phonons (Bose fields) coupled to two-level systems (spin systems). We have investigated the zero-temperature phase diagram for the localization-delocalization transition of a tunneling particle interacting with an Ohmic heat bath. Our results are compared with known existing approximate treatments. A modified phase diagram using the displaced squeezed state is presented.

Novel correlations in two dimensions: Some exact solutions

We construct a new many-body Hamiltonian with two- and three-body interactions in two space dimensions and obtain its exact many-body ground state for an arbitrary number of particles. This ground state has a novel pairwise correlation. A class of exact solutions for the excited states is also found. These excited states display an energy spectrum similar to the Calogero-Sutherland model in one dimension. The model reduces to an analog of the well-known trigonometric Sutherland model when projected on to a circular ring.

Quantum-confinement effects on the ordering of the lowest-lying excited states in conjugated chains

The symmetrized density-matrix renormalization-group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation delta) to study the ordering of the lowest one-photon (1(1)B(u)(-)) and two-photon (2(1)A(g)(+)) states in one-dimensional conjugated systems with chain lengths N up to N = 80 sites. Three different types of crossovers are studied, as a function of U/t, delta, and N. The ''U crossover'' emphasizes the larger ionic character of the 2A(g) state compared to the lowest triplet excitation. The ''delta crossover'' shows strong dependence on both N and U/t. the ''N crossover'' illustrates the more localized nature of the 2A(g) excitation relative to the 1B(u) excitation at intermediate correlation strengths.

The two-step positive temperature coefficient in resistance characteristics of n-(Ba,Pb)TiO3 ceramics created through inclusion of grain boundary modifier additives

Donor-doped n-(Ba,Pb)TiO3 polycrystalline ceramics exhibit distinctly two-step positive temperature coefficient of resistance (PTCR) characteristics when formulated with suitable combinations of B2O3 and Al2O3 as grain boundary modifiers by heterogeneous addition. B2O3 or Al2O3 when added singularly resulted in either steep or broad PTCR jumps respectively across the phase transition. The two-step PTCR is attributed to the activation of the acceptor states, created through B2O3 and Al2O3, for various temperature regimes above the Curie point (T-c). The changing pattern of trap states is evident from the presence of Ti4+-O--Al3+ type hole centres in the grain boundary layer regions, identified in the electron paramagnetic resonance (EPR) spectra. That charge redistribution occurs among the inter-band gap defect states on crossing the Curie temperature is substantiated by the temperature coefficient in the EPR results. Capacitance-voltage results clearly show that there is an increase in the density of trap states with the addition of B2O3 and Al2O3. The spread in energy values of these trap states is evident from the large change in barrier height (phi similar or equal to 0.25-0.6 eV) between 500 and 650 K.

Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin Hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground-state configuration of all the members of the family on a periodic chain. The ground state is twofold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh Hamiltonian with a twofold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.

Denaturant mediated unfolding of both native and molten globule states of maltose binding protein are accompanied by large [Delta]Cp's

Maltose binding protein (MBP) is a large, monomeric two domain protein containing 370 amino acids. In the absence of denaturant at neutral pH, the protein is in the native state, while at pH 3.0 it forms a molten globule. The molten globule lacks a tertiary circular dichroism signal but has secondary structure similar to that of the native state. The molten globule binds 8-anilino-1-naphthalene sulfonate (ANS). The unfolding thermodynamics of MBP at both pHs were measured by carrying out a series of isothermal urea melts at temperatures ranging from 274–329 K. At 298 K, values of [Delta]G°, [Delta]Cp, and Cm were 3.1 ± 0.2 kcal mol−1, 5.9 ± 0.8 kcal mol−1 K−1 (15.9 cal (mol-residue)−1 K−1), and 0.8 M, respectively, at pH 3.0 and 14.5 ± 0.4 kcal mol−1, 8.3 ± 0.7 kcal mol−1 K−1 (22.4 kcal (mol-residue)−1 K−1), and 3.3 M, respectively, at pH 7.1. Guanidine hydrochloride denaturation at pH 7.1 gave values of [Delta]G° and [Delta]Cp similar to those obtained with urea. The m values for denaturation are strongly temperature dependent, in contrast to what has been previously observed for small globular proteins. The value of [Delta]Cp per mol-residue for the molten globule is comparable to corresponding values of [Delta]Cp for the unfolding of typical globular proteins and suggests that it is a highly ordered structure, unlike molten globules of many small proteins. The value of [Delta]Cp per mol-residue for the unfolding of the native state is among the highest currently known for any protein.

Two-Stage Extended Kalman Filters with Derivative-Free Local Linearizations

This paper proposes a derivative-free two-stage extended Kalman filter (2-EKF) especially suited for state and parameter identification of mechanical oscillators under Gaussian white noise. Two sources of modeling uncertainties are considered: (1) errors in linearization, and (2) an inadequate system model. The state vector is presently composed of the original dynamical/parameter states plus the so-called bias states accounting for the unmodeled dynamics. An extended Kalman estimation concept is applied within a framework predicated on explicit and derivative-free local linearizations (DLL) of nonlinear drift terms in the governing stochastic differential equations (SDEs). The original and bias states are estimated by two separate filters; the bias filter improves the estimates of the original states. Measurements are artificially generated by corrupting the numerical solutions of the SDEs with noise through an implicit form of a higher-order linearization. Numerical illustrations are provided for a few single- and multidegree-of-freedom nonlinear oscillators, demonstrating the remarkable promise that 2-EKF holds over its more conventional EKF-based counterparts. DOI: 10.1061/(ASCE)EM.1943-7889.0000255. (C) 2011 American Society of Civil Engineers.

A five level inverter scheme with common mode volatge elimination by cascading conventional two level and three level NPC inverters for an induction motor drive

Common-mode voltage generated by the PWM inverter causes shaft voltage, bearing current and ground leakage current in induction motor drive system, resulting in an early motor failure. This paper presents a common-mode elimination scheme for a five-level inverter with reduced power circuit complexity. The proposed scheme is realised by cascading conventional two-level and conventional NPC three-level inverters in conjunction with an open-end winding three-phase induction motor drive and the common-mode voltage (CMV) elimination is achieved by using only switching states that result in zero CMV, for the entire modulation range.

Two-timescale Q-learning Algorithms with an Application to Routing in Networks

We propose two variants of the Q-learning algorithm that (both) use two timescales. One of these updates Q-values of all feasible state-action pairs at each instant while the other updates Q-values of states with actions chosen according to the ‘current ’ randomized policy updates. A sketch of convergence of the algorithms is shown. Finally, numerical experiments using the proposed algorithms for routing on different network topologies are presented and performance comparisons with the regular Q-learning algorithm are shown.

Nature of Electronic States in Atomically Thin MoS(2) Field-Effect Transistors

We present low-temperature electrical transport experiments in five field-effect transistor devices consisting of monolayer, bilayer, and trilayer MoS(2) films, mechanically exfoliated onto Si/SiO(2) substrate. Our experiments reveal that the electronic states In all films are localized well up to room temperature over the experimentally accessible range of gate voltage. This manifests in two-dimensional (2D) variable range hopping (VRH) at high temperatures, while below similar to 30 K, the conductivity displays oscillatory structures In gate voltage arising from resonant tunneling at the localized sites. From the correlation energy (T(0)) of VRH and gate voltage dependence of conductivity, we suggest that Coulomb potential from trapped charges In the substrate is the dominant source of disorder in MoS(2) field-effect devices, which leads to carrier localization, as well.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice. We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation eta and eta + d eta, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary.

Quantum fidelity for one-dimensional Dirac fermions and two-dimensional Kitaev model in the thermodynamic limit

We study the scaling behavior of the fidelity (F) in the thermodynamic limit using the examples of a system of Dirac fermions in one dimension and the Kitaev model on a honeycomb lattice.We show that the thermodynamic fidelity inside the gapless as well as gapped phases follow power-law scalings, with the power given by some of the critical exponents of the system. The generic scaling forms of F for an anisotropic quantum critical point for both the thermodynamic and nonthermodynamic limits have been derived and verified for the Kitaev model. The interesting scaling behavior of F inside the gapless phase of the Kitaev model is also discussed. Finally, we consider a rotation of each spin in the Kitaev model around the z axis and calculate F through the overlap between the ground states for the angle of rotation η and η + dη, respectively. We thereby show that the associated geometric phase vanishes. We have supplemented our analytical calculations with numerical simulations wherever necessary