Weakly Non-Ergodic Statistical Physics

For weakly non ergodic systems, the probability density function of a time average observable is where is the value of the observable when the system is in state j=1,…L. p _j ^eq is the probability that a member of an ensemble of systems occupies state j in equilibrium. For a particle undergoing a fractional diffusion process in a binding force field, with thermal detailed balance conditions, p _j ^eq is Boltzmann’s canonical probability. Within the unbiased sub-diffusive continuous time random walk model, the exponent 0<α<1 is the anomalous diffusion exponent 〈x ²〉∼t ^α found for free boundary conditions. When α→1 ergodic statistical mechanics is recovered . We briefly discuss possible physical applications in single particle experiments.     

Global entanglement and coherent states in an {\sf N}-partite system

We consider a quantum system consisting of N parts, each of which is a “quKit” described by a K dimensional Hilbert space. We prove that in the symmetric subspace, , a pure state is not globally entangled, if and only if it is a coherent state. It is also shown that in the orthogonal complement all states are globally entangled.     

The one-body and two-body density matrices of finite nuclei with an appropriate treatment of the center-of-mass motion⋆

The one-body and two-body density matrices in coordinate space and their Fourier transforms in momentum space are studied for a nucleus (a nonrelativistic, self-bound finite system). Unlike the usual procedure, suitable for infinite or externally bound systems, they are determined as expectation values of appropriate intrinsic operators, dependent on the relative coordinates and momenta (Jacobi variables) and acting on intrinsic wave functions of nuclear states. Thus, translational invariance (TI) is respected. When handling such intrinsic quantities, we use an algebraic technique based upon the Cartesian representation, in which the coordinate and momentum operators are linear combinations of the creation and annihilation operators and for oscillator quanta. Each of the relevant multiplicative operators can then be reduced to the form: one exponential of the set { } times another exponential of the set { }. In the course of such a normal-ordering procedure we offer a fresh look at the appearance of “Tassie-Barker” factors, and point out other model-independent results. The intrinsic wave function of the nucleus in its ground state is constructed from a nontranslationally-invariant (nTI) one via existing projection techniques. As an illustration, the one-body and two-body momentum distributions (MDs) for the ⁴He nucleus are calculated with the Slater determinant of the harmonic-oscillator model as the trial, nTI wave function. We find that the TI introduces quite important effects in the MDs.     

On the Meissner effect in a superconductor with 4-fermion attraction

A presence of a Meissner-Ochsenfeld effect in a gas of spin 1/2 fermions with an interaction , where is a volume of a region in real space which is taken by thesystem and with , satisfying Fermi anticommutation relations, is investigated. The effect proves to be weaker than in BCS by a factor 3/4 at T = 0, implying a greater penetration depth of external magnetic field. V ₄ is nonzero only within a thin layer of 1-fermion energies around the chemical potential .Received: 14 June 2004, Published online: 12 October 2004PACS: 74.20.-z Theories and models of superconducting state - 74.20.Fg BCS theory and its development     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization     

Terahertz generation by nonlinear mixing of laser and its second harmonic in a rippled density plasma

Terahertz radiation generation by second-order nonlinear mixing of laser $ (\omega_{1} ,\,\vec{k}_{1} ) $ and its frequency shifted second harmonic $ \omega_{2} = 2\omega_{1} - \omega ,\,\,\vec{k}_{2} \, $ $ (\omega \ll \omega_{1} ) $ in a plasma, in the presence of an obliquely inclined density ripple of wave number $ \vec{q} $ , are investigated. The lasers exert ponderomotive force on electrons and drive density perturbations at $ (2\omega_{1} ,\,2\vec{k}_{1} - \vec{q}) $ and $ (\omega_{1} - \omega_{2} ,\,\vec{k}_{1} - \vec{k}_{2} - \vec{q}) $ . These perturbations beat with the electron oscillatory velocities due to the lasers to produce a nonlinear current at $ \omega ,\,\vec{k} = 2\vec{k}_{1} - \vec{k}_{2} - \vec{q} $ , resonantly driving the terahertz radiation when $ \vec{q} $ satisfies the phase matching condition. The radiated THz intensity depends on the relative polarization of the lasers and scales as the square of intensity of the fundamental laser and linearly with the square root of the intensity of the second harmonic. The THz emission is maximized when the polarization of the lasers is aligned. These results are consistent with the recent experimental results.     

Local Eigenvalue Density for General MANOVA Matrices

We consider random n×n matrices of the form $$\begin{aligned} \left( XX^*+YY^*\right)^{-\frac{1}{2}}YY^*\left( XX^*+YY^*\right )^{-\frac{1}{2}} , \end{aligned}$$ where X and Y have independent entries with zero mean and variance one. These matrices are the natural generalization of the Gaussian case, which are known as MANOVA matrices and which have joint eigenvalue density given by the third classical ensemble, the Jacobi ensemble. We show that, away from the spectral edge, the eigenvalue density converges to the limiting density of the Jacobi ensemble even on the shortest possible scales of order 1/n (up to logn factors). This result is the analogue of the local Wigner semicircle law and the local Marchenko-Pastur law for general MANOVA matrices.     

Dynamics of a two-level system coupled to Ohmic bath: a perturbation approach

The quantum dynamics, both non-equilibrium and equilibrium, of the dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. It works well for the whole parameter range and and our main results are: the coherence-incoherence transition is at ; for the non-equilibrium correlation ; the susceptibility is of a double peak structure for and the Shibas relation is exactly satisfied; at the transition point the equilibrium correlation in the long time limit.Received: 14 October 2003, Published online: 8 June 2004PACS: 72.20.Dp General theory, scattering mechanisms - 05.30.-d Quantum statistical mechanics     

$\mathsf{\sqrt{3}}$ linear structures in the Te/Ni(111) system

Surface structures in the Te/Ni(111) system are revealed by using reflection high-energy electron diffraction combined with X-ray and ultraviolet photoelectron spectroscopies. At a 0.33 mono-layer (ML)-Te/Ni(111) surface, a reversible structural phase transition is observed with a transition temperature T_c of 380 C. The diffraction pattern from the low temperature phase is accompanied by streaks. The high and low temperature phases are characterized by and rectangle, respectively. The mechanism of the phase transition is explained by the order-disorder transition with a rumpled chain model. Both 0.51 ML- and 0.44 ML-Te/Ni(111) surfaces exhibit the complex diffraction patterns accompanied by diffuse streaks. These surface structures are characterized by the rectangle and , respectively. All diffuse streaks obtained at the above surfaces are consistently interpreted in the view of the ill-ordered arrangements of the well-ordered linear chains. It is shown that the linear structure is the key in the Te/Ni(111) system.Received: 1 December 2003, Published online: 20 April 2004PACS: 61.14.Hg Low-energy electron diffraction (LEED) and reflection high-energy electron diffraction (RHEED) - 68.65.-k Low-dimensional, mesoscopic, and nanoscale systems: structure and nonelectronic properties - 64.60.Cn Order-disorder transformations; statistical mechanics of model systems     

Full counting statistics of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of , A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.Received: 30 June 2003, Published online: 15 October 2003PACS: 73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)     

Features of chemical reactions at vanishing kinetic energy: the presence of internally “hot” reagents

The reactions between vibrationally and rotationally excited H₂ and D₂ molecules and the F atom are analyzed at ultra-low collision energies using the Coupled Channels quantum approach. The aim of this work is to compare the relative efficiency of the reactive scattering event with that of the vibrational or rotational quenching process in the ultra-cold temperature regime in order to establish general trends, possibly amenable to experiments on this or on more complex systems. We have already compared the rotational de-excitation efficiency with the reactive one in the reaction [1] and we have seen in that case that rotational de-excitation is more efficient than reaction when going down to ultra-low energies. We are investigating here the vibrational excitation case when the internal energy of the molecule becomes large enough to be above the classical barrier, and we are also presenting new results for the rotationally hot H₂ partner. We find that, with vibrationally hot molecules, the reaction becomes more efficient than the relaxation process, while the relative efficiency of such processes when having rotationally hot molecular partners is much more system-dependent.Received: 15 June 2004, Published online: 7 September 2004PACS: 34.10. + x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) - 34.50.Lf Chemical reactions, energy disposal, and angular distribution, as studied by atomic and molecular beams - 34.20.Mq Potential energy surfaces for collisions     

Surface critical behavior of fluids: Lennard-Jones fluid near a weakly attractive substrate

The phase behavior of fluids near weakly attractive substrates is studied by computer simulations of the coexistence curve of a Lennard-Jones (LJ) fluid confined in a slitlike pore. The temperature dependence of the density profiles of the LJ fluid was used to study the surface critical behavior. A universal critical behavior of the local order parameter, defined as the difference between the local densities of the coexisting liquid and vapor phases at some distance from the pore walls, , is observed in a wide temperature range and found to be consistent with the surface critical behavior of the Ising model. Near the surface the dependence of the order parameter on the reduced temperature obeys a scaling law ~1 with a critical exponent 1 of about 0.8, corresponding to the surface transition. A crossover from bulk-like to surface-like critical behavior occurs, when the distance to the surface is about twice the correlation length at the given temperature. Relations between the and transitions in Ising systems and the surface critical behavior of fluids are discussed.     

Molecular dynamics in nanophase-separated comb-like poly( $ \upalpha$- n-alkyl $ \upbeta$-L-aspartate)s

A series of poly( -n-alkyl -L-aspartates) which are nanophase self-assembled comb-like polymers has been studied by dielectric spectroscopy in a broad frequency range ( 10^-23×10⁶ Hz), with n-alkyls side chains of various lengths, 10n18. In every member of the series the same relaxations were identified after the decomposition of the experimental isothermal trace in up to three peaks with relaxation times distributions. The strength, width and average relaxation time for all the relaxation modes were determined for each material. Besides the local low temperature, Arrhenius modes, two relaxation modes, and , present a cooperative character whose dynamics are not affected by the side chains melting. The relaxation is a polyethylene-like glass transition of the amorphous side chains and its dynamics is strongly dependent on the n value due to the increasing restrictions imposed by the self-assembled confinement. The strength of the relaxation mode increases as the lateral chains loose their 2D order. The restricted chopstick motion of the rigid rods is thought to be the origin of the mode; this motion is hindered at temperatures where the cage size decreases as a result of the increasing disorder with temperature.     

Random matrix theory and equilibrium statistics for the quasienergies of classically chaotic systems

We calculate thek-level correlation function for the eigenphases of theN-dimensional Floquet operator of kicked dynamics whose classical counterpart is chaotic in the limitN by applying standard equilibrium statistical mechanics to a fictitiousN-particle system which is constructed from the eigenvalue equation of the Floquet operator and show that they become equal to those of random matrices from the circular ensemble associated with the appropriate universality class.     

A time convolution less density matrix approach to the nonlinear optical response of a coupled system-bath complex

Time convolution less density matrix theory (TCL) is a powerful and well established tool to investigate strong system-bath coupling for linear optical spectra. We show that TCL equations can be generalised to the nonlinear optical response up to a chosen order in the optical field. This goal is achieved via an time convolution less perturbation scheme for the reduced density matrices of the electronic system. In our approach, the most important results are the inclusion of a electron-phonon coupling non-diagonal in the electronic states and memory effects of the bath: First, the considered model system is introduced. Second, the time evolution of the statistical operator is expanded with respect to the external optical field. This expansion is the starting point to explain how a TCL theory can treat the response up to in a certain order in the external field. Third, new TCL equations, including bath memory effects, are derived and the problem of information loss in the reduced density matrix is analysed. For this purpose, new dimensions are added to the reduced statistical operator to compensate lack of information in comparison with the full statistical operator. The theory is benchmarked with a two level system and applied to a three level system including non-diagonal phonon coupling. In our analysis of pump-probe experiments, the bath memory is influenced by the system state occupied between pump and probe pulse. In particular, the memory of the bath influences the dephasing process of electronic coherences developing during the time interval between pump and probe pulses.     

Diffusion or bounce back in relativistic heavy-ion collisions?

The time evolution of pseudorapidity distributions of produced charged hadrons in d + Au collisions at = 200 GeV is investigated. Results of a nonequilibrium statistical relativistic diffusion model with three sources are compared with a macroscopic “bounce-back” model that does not allow for statistical equilibration at large times, but instead leads to motion reversal. When compared to the data, the results of the diffusion approach are more precise, thus emphasizing that the system is observed to be on its way to thermal equilibrium.     

The Curious Nonexistence of Gaussian 2-Designs

Ensembles of pure quantum states whose 2nd moments equal those of the unitarily uniform Haar ensemble—2-designs—are optimal solutions for several tasks in quantum information science, especially state and process tomography. We show that Gaussian states cannot form a 2-design for the continuous-variable (quantum optical) Hilbert space ${L^2(\mathbb{R})}$ . This is surprising because the affine symplectic group HWSp (the natural symmetry group of Gaussian states) is irreducible on the symmetric subspace of two copies. In finite dimensional Hilbert spaces, irreducibility guarantees that HWSp-covariant ensembles (such as mutually unbiased bases in prime dimensions) are always 2-designs. This property is violated by continuous variables for a subtle reason: the (well-defined) HWSp-invariant ensemble of Gaussian states does not have a density matrix because its defining integral does not converge. In fact, no Gaussian ensemble is even close (in a precise sense) to being a 2-design. This surprising difference between discrete and continuous quantum mechanics has important implications for optical state and process tomography.     

Measurement of the μ decay spectrum with the ICARUS liquid Argon TPC

Examples are given which prove the ICARUS detector quality through relevant physics measurements. We study the decay energy spectrum from a sample of stopping events acquired during the test run of the ICARUS T600 detector. This detector allows the spatial reconstruction of the events with fine granularity, hence, the precise measurement of the range and dE/dx of the with high sampling rate. This information is used to compute the calibration factors needed for the full calorimetric reconstruction of the events. The Michel parameter is then measured by comparison of the experimental and Monte Carlo simulated decay spectra, obtaining . The energy resolution for electrons below MeV is finally extracted from the simulated sample, obtaining .Received: 20 November 2003, Published online: 4 February 2004     

Changes in the mean square charge radii of neutron-deficient europium isotopes measured by the laser ion source resonance ionization spectroscopy

The laser ion source has been used for the study of the isotope shifts of neutron-deficient Eu isotopes. The extension of the region of applicability of the method by using the - and -radiation detection is reported. We have measured the isotope shifts of the europium optical line 576.520 nm for . To increase the laser ion source efficiency an axial magnetic field (350 gauss) was applied. Nearly a twofold rise of the ionization efficiency for Eu was observed. By using the effect of optical ion bunching an increase of the selectivity was obtained. The isotope shift data for are in agreement with the previously measured isotope shifts for these nuclides. The new data for and refined data for point to a gradual increase of the deformation for these isotopes. Comparisons with microscopic-macroscopic calculations and calculations in the framework of the Hartree-Fock model were performed.Received: 10 November 2003, Revised: 28 April 2004, Published online: 19 October 2004PACS: 29.25.Rm Sources of radioactive nuclei - 42.62.Fi Laser spectroscopy - 21.10.-k Properties of nuclei; nuclear energy levels - 21.10.Ft Charge distribution