The quantum measurement process in an exactly solvable model

An exactly solvable model for a quantum measurement is discussed which is governed by hamiltonian quantum dynamics. The $z$-component $\hat s_z$ of a spin-1/2 is measured with an apparatus, which itself consists of magnet coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state according to the sign of $s_z$ of the tested spin. The quantum measurement goes in two steps. On a timescale $1/\sqrt{N}$ the off-diagonal elements of the spin's density matrix vanish due to a unitary evolution of the tested spin and the $N$ apparatus spins; on a larger but still short timescale this is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is a quantum process which can already be understood from classical statistical mechanics. The von Neumann collapse and the Born rule are derived rather than postulated.Comment: 7 pages revtex, 2 figure

New Bardeen-Cooper-Schrieffer-type theory at finite temperature with particle-number conservation

We formulate a new Bardeen-Cooper-Schrieffer (BCS)-type theory at finite temperature, by deriving a set of variational equations of the free energy after the particle-number projection. With its broad applicability, this theory can be a useful tool for investigating the pairing phase transition in finite systems with the particle-number conservation. This theory provides effects of the symmetry-restoring fluctuation (SRF) for the pairing phenomena in finite fermionic systems, distinctively from those of additional quantum fluctuations. It is shown by numerical calculations that the phase transition is compatible with the conservation in this theory, and that the SRF shifts up the critical temperature ($T^\mathrm{cr}$). This shift of $T^\mathrm{cr}$ occurs due to reduction of degrees-of-freedom in canonical ensembles, and decreases only slowly as the particle-number increases (or as the level spacing narrows), in contrast to the conventional BCS theory.Comment: 10 pages including 3 figures, to be published in Phys. Rev.

Mean-field theory of quantum brownian motion

We investigate a mean-field approach to a quantum brownian particle interacting with a quantum thermal bath at temperature $T$, and subjected to a non-linear potential. An exact, partially classical description of quantum brownian motion is proposed, which uses negative probabilities in its intermediate steps. It is shown that properties of the quantum particle can be mapped to those of two classical brownian particles in a common potential, where one of them interacts with the quantum bath, whereas another one interacts with a classical bath at zero temperature. Due to damping the system allows a unique and non-singular classical limit at $\hbar \to 0$. For high $T$ the stationary state becomes explicitly classical. The low-temperature case is studied through an effective Fokker-Planck equation. Non-trivial purely quantum correlation effects between the two particles are found.Comment: 13 pages, 0 figures, revte

The quantum measurement process: an exactly solvable model

An exactly solvable model for a quantum measurement is discussed, that integrates quantum measurements with classical measurements. The z-component of a spin-1/2 test spin is measured with an apparatus, that itself consists of magnet of N spin-1/2 particles, coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state, according to the sign of s_z of the test spin. The quantum measurement goes in two steps. On a timescale 1/\sqrt{N} the collapse takes place due to a unitary evolution of test spin and apparatus spins; on a larger but still short timescale this collapse is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is basically a classical process, that can already be understood from classical statistical mechanics.Comment: 4 pages, presented at the conference "Anomalies and Strange Behavior in Physics: Challenging the conventional", Napels, April, 2003. v2: Elaboration on the statistical interpretation of Q

Quantum thermodynamics: thermodynamics at the nanoscale

A short introduction on quantum thermodynamics is given and three new topics are discussed: 1) Maximal work extraction from a finite quantum system. The thermodynamic prediction fails and a new, general result is derived, the ``ergotropy''. 2) In work extraction from two-temperature setups, the presence of correlations can push the effective efficiency beyond the Carnot bound. 3) In the presence of level crossing, non-slow changes may be more optimal than slow ones.Comment: 5 pages. Talk given at Physics of Quantum Electronics (PQE2004), Snowbird, by Th.M. Nieuwenhuize

Billiard Systems in Three Dimensions: The Boundary Integral Equation and the Trace Formula

We derive semiclassical contributions of periodic orbits from a boundary integral equation for three-dimensional billiard systems. We use an iterative method that keeps track of the composition of the stability matrix and the Maslov index as an orbit is traversed. Results are given for isolated periodic orbits and rotationally invariant families of periodic orbits in axially symmetric billiard systems. A practical method for determining the stability matrix and the Maslov index is described.Comment: LaTeX, 19 page

Does the quark-gluon plasma contain stable hadronic bubbles?

We calculate the thermodynamic potential of bubbles of hadrons embedded in quark-gluon plasma, and of droplets of quark-gluon plasma embedded in hadron phase. This is a generalization of our previous results to the case of non-zero chemical potentials. As in the zero chemical potential case, we find that a quark-gluon plasma in thermodynamic equilibrium may contain stable bubbles of hadrons of radius $R \simeq 1$ fm. The calculations are performed within the MIT Bag model, using an improved multiple reflection expansion. The results are of relevance for neutron star phenomenology and for ultrarelativistic heavy ion collisions.Comment: 12 pages including 8 figures. To appear in Phys. Rev.

Casimir Effects: An Optical Approach I. Foundations and Examples

We present the foundations of a new approach to the Casimir effect based on classical ray optics. We show that a very useful approximation to the Casimir force between arbitrarily shaped smooth conductors can be obtained from knowledge of the paths of light rays that originate at points between these bodies and close on themselves. Although an approximation, the optical method is exact for flat bodies, and is surprisingly accurate and versatile. In this paper we present a self-contained derivation of our approximation, discuss its range of validity and possible improvements, and work out three examples in detail. The results are in excellent agreement with recent precise numerical analysis for the experimentally interesting configuration of a sphere opposite an infinite plane.Comment: Minor corrections. Submitted to Nucl. Phys.

Obstructive Sleep Apnea Syndrome (OSAS) treated with orthodontic appliances in children : a new feasible approach

Obstructive Sleep Apnea Syndrome (OSAS) affects up to 4% of the paediatric population and, due to the high risk of cardio-vascular and neurological complications and negative outcomes on the developmental process associated, represents the most serious type of Sleep Disordered Breathing (SDB) and the most challenging for public health.Although the most common treatment for OSAS in childhood is Adenotonsillectomy (AT), this approach is limited by its surgical risks and by a high prevalence of recurrence or partial success, with persistence of signs and symptoms of obstructive apnea.The presence of cranio-facial abnormalities and malocclusion is considered an important risk factor for paediatric OSAS and its recurrence after AT. Children affected by OSAS often present specific oro-facial features such asnarrow maxilla, mandibular retrusion, anterior openbite, bilateral/ monolateral cross bite, that are frequently associated with dysfunctions such as oral breathing and atypical swallowing. Those alterations can represent an anatomical base which can contribute to the development of paediatric OSAS, especially in preschool child aged 3-6 years, when the hyperplasia of adenoids and tonsils is reported to be at its peak with a higher risk for obstruction. The purpose of the present research is to evaluate the possibility that an orthodontic treatment, primary aiming to the treatment of malocclusion and the related dysfunctions, can induce improvement or relief of respiratory nighttime distress, as a secondary effect. The sample consisted of 5 children affected by OSAS, 3 female and 2 male, average aged 4.5 years, who have never undergone AT or have had a recurrence of sign and symptoms 1 year after AT.All patients presented narrow maxilla, associated with monolateral/ bilateral crossbite and or anterior openbite. The patients underwent orthodontic treatment performed with an elastodontic appliance, which is a removable oral device made of PVC and widely used in children aged less than 6 years. The following variables were evaluated in each patient at the beginning (T0) and after 1 year (T2) of orthodontic treatment:occlusal parameters; Sleep Clinical Score (SCS); Night time poligraphic parameters: Snoring, Apnea/Hypopnea Index (AHI) andOswestry Disability Index (ODI).Four out of 5 patients showed high compliance to the orthodontic treatment and improved their occlusal relationship. In those patients also AHI and ODI index improved as well as the SCS score, revealing a reduction of sign and symptoms of OSAS. The only patient who did not improve his occlusal and respiratory findings also showed poor compliance to the orthodontic treatment. The study suggest that the treatment of malocclusion might produce improvements in sign and symptoms of OSAS in children aged 3-6 years and that preformed elastodontc appliances are a feasible therapeutic tool for this purpose