Search results for "Quantum statistical mechanics"
showing 10 items of 41 documents
The Dynamical Problem for a Non Self-adjoint Hamiltonian
2012
After a compact overview of the standard mathematical presentations of the formalism of quantum mechanics using the language of C*- algebras and/or the language of Hilbert spaces we turn attention to the possible use of the language of Krein spaces.I n the context of the so-called three-Hilbert-space scenario involving the so-called PT-symmetric or quasi- Hermitian quantum models a few recent results are reviewed from this point of view, with particular focus on the quantum dynamics in the Schrodinger and Heisenberg representations.
Classical and Quantum Two-Dimensional Fluids in the Gibbs Ensemble
1994
We study the properties of model fluids in two spatial dimensions with Gibbs ensemble Monte Carlo (GEMC) techniques. In particular in the first part of the paper we study the entropy driven phase separation in case of a nonadditive symmetric hard disc fluid and locate by a combination of GEMC with finite size scaling techniques the critical line of nonadditivities as a function of the system density, which separates the mixing/demixing regions, we compare with a simple approximation. In the second part we successfully combine path integral Monte Carlo (PIMC) and GEMC techniques in order to locate the gas-liquid coexistence densities for a fluid with classical degrees of freedom and internal…
Similarity Solutions and Collapse in the Attractive Gross-Pitaevskii Equation
2000
We analyse a generalised Gross-Pitaevskii equation involving a paraboloidal trap potential in $D$ space dimensions and generalised to a nonlinearity of order $2n+1$. For {\em attractive} coupling constants collapse of the particle density occurs for $Dn\ge 2$ and typically to a $\delta$-function centered at the origin of the trap. By introducing a new dynamical variable for the spherically symmetric solutions we show that all such solutions are self-similar close to the center of the trap. Exact self-similar solutions occur if, and only if, $Dn=2$, and for this case of $Dn=2$ we exhibit an exact but rather special D=1 analytical self-similar solution collapsing to a $\delta$-function which …
Statistical Mechanics of the Integrable Models
1987
There is an infinity of classically integrable models. The only ones we can consider here, and these only briefly, are: the sine-Gordon (s-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sin \phi ,$$ (1.1) the sinh-Gordon (sinh-G) model $${\phi _{{\rm{xx}}}}{}^ - {\phi _{{\rm{tt}}}} = {{\rm{m}}^2}\sinh \phi ,$$ (1.2) and the repulsive and attractive non-linear Schrodinger (NLS) models $${}^ - {\rm{i}}{\phi _{\rm{t}}} = {\phi _{{\rm{xx}}}}{}^ - 2{\rm{c}}\phi {\left| \phi \right|^2}.$$ (1.3) The “attractive” NLS has real coupling constant c 0; φ is complex. In (1.1) and (1.2) m is a mass (ħ = c = 1) and φ is real. These 4 integrable models are in one space and one time …
Quantum and Classical Statistical Mechanics of the Non-Linear Schrödinger, Sinh-Gordon and Sine-Gordon Equations
1985
We are going to describe our work on the quantum and classical statistical mechanics of some exactly integrable non-linear one dimensional systems. The simplest is the non-linear Schrodinger equation (NLS) $$i{\psi _t} = - {\psi _{XX}} + 2c{\psi ^ + }\psi \psi $$ (1) where c, the coupling constant, is positive. The others are the sine- and sinh-Gordon equations (sG and shG) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sin \phi $$ (1.2) $${\phi _{xx}} - {\phi _{tt}} = {m^2}\sinh \phi $$ (1.3)
Geometric phase induced by a cyclically evolving squeezed vacuum reservoir
2006
We propose a new way to generate an observable geometric phase by means of a completely incoherent phenomenon. We show how to imprint a geometric phase to a system by "adiabatically" manipulating the environment with which it interacts. As a specific scheme we analyse a multilevel atom interacting with a broad-band squeezed vacuum bosonic bath. As the squeezing parameters are smoothly changed in time along a closed loop, the ground state of the system acquires a geometric phase. We propose also a scheme to measure such geometric phase by means of a suitable polarization detection.
Wick Theorem for General Initial States
2012
We present a compact and simplified proof of a generalized Wick theorem to calculate the Green's function of bosonic and fermionic systems in an arbitrary initial state. It is shown that the decomposition of the non-interacting $n$-particle Green's function is equivalent to solving a boundary problem for the Martin-Schwinger hierarchy; for non-correlated initial states a one-line proof of the standard Wick theorem is given. Our result leads to new self-energy diagrams and an elegant relation with those of the imaginary-time formalism is derived. The theorem is easy to use and can be combined with any ground-state numerical technique to calculate time-dependent properties.
Local dynamics and phase transition in quantum paraelectric SrTiO3 studied by Ti K-edge x-ray absorption spectroscopy
2016
Strontium titanate is a model quantum paraelectric in which, in the region of dominating quantum statistics, the ferroelectric instability is inhibited due to nearly complete compensation of the harmonic contribution into ferroelectric soft mode frequency by the zero- point motion contribution. The enhancement of atomic masses by the substitution of 16 O with 18O decreases the zero-point atomic motion, and low-T ferroelectricity in SrTi18O3 is realized. In this study we report on the local structure of Ti in SrTi16O3 and SrTi18O3 investigated by Extended X-ray Absorption Fine Structure measurements in the temperature range 6 - 300 K.
Lindblad equation approach for the full counting statistics of work and heat in driven quantum systems
2013
We formulate the general approach based on the Lindblad equation to calculate the full counting statistics of work and heat produced by driven quantum systems weakly coupled with a Markovian thermal bath. The approach can be applied to a wide class of dissipative quantum systems driven by an arbitrary force protocol. We show the validity of general fluctuation relations and consider several generic examples. The possibilities of using calorimetric measurements to test the presence of coherence and entanglement in the open quantum systems are discussed. QC 20141010
Nonequilibrium Green's function approach to strongly correlated few-electron quantum dots
2009
The effect of electron-electron scattering on the equilibrium properties of few-electron quantum dots is investigated by means of nonequilibrium Green's function theory. The ground and equilibrium states are self-consistently computed from the Matsubara (imaginary time) Green's function for the spatially inhomogeneous quantum dot system whose constituent charge carriers are treated as spin-polarized. To include correlations, the Dyson equation is solved, starting from a Hartree-Fock reference state, within a conserving (second-order) self-energy approximation where direct and exchange contributions to the electron-electron interaction are included on the same footing. We present results for…