Boltzmann Factor Exp Research Articles

Observation of the continuous transformation of a four level laser into a two level system

A longstanding and fundamental question of laser and maser physics concerns the energy separation (Δϵ) required between the pumped and lasing states of a three (or four) level system. We observe a four level laser gradually transform into a two level (nonlasing) system by photoassociating Cs-Ar thermal atomic pairs and monitoring subsequent stimulated emission on the 6p2P3/2 → 6s2S1/2 (D2) transition of Cs at 852.1 nm. Laser excitation spectra demonstrate that the value of Δϵ below which the system rapidly assumes the form of a two level structure and lasing ceases is ∼0.7kT which corresponds to a Boltzmann factor (exp[−Δϵ/kT]) of 0.5.

Ion Transport with Charge-Protected and Non-Charge-Protected Cations in Alcohol-Based Electrolytes Using the Compensated Arrhenius Formalism. Part I: Ionic Conductivity and the Static Dielectric Constant

The temperature dependence of ionic conductivity and the static dielectric constant is examined for 0.30 m TbaTf- or LiTf-1-alcohol solutions. Above ambient temperature, the conductivity increases with temperature to a greater extent in electrolytes whose salt has a charge-protected cation. Below ambient temperature, the dielectric constant changes only slightly with temperature in electrolytes whose salt has a cation that is not charge-protected. The compensated Arrhenius formalism is used to describe the temperature-dependent conductivity in terms of the contributions from both the exponential prefactor σo and Boltzmann factor exp(-Ea/RT). This analysis explains why the conductivity decreases with increasing temperature above 65 °C for the LiTf-dodecanol electrolyte. At higher temperatures, the decrease in the exponential prefactor is greater than the increase in the Boltzmann factor.

Biophysical connection between evolutionary dynamics and thermodynamics in in vitro evolution

We analyzed a mathematical model of in vitro evolution conducted by repetition of mutagenesis and selection processes. The selection process consists of the selective enrichment and subsequent sampling as follows: each mutant with fitness W is amplified by the Boltzmann factor exp ( rW / k B T the ) , where the fitness W is defined as the negative Gibbs free energy ( − Δ G ) in a reaction of the phenotypic molecules and r is the round number of the selective enrichment; then, an arbitrary mutant is randomly chosen from the resulting mutant population and it becomes a new parent in the next generation. As a result, we found that the evolutionary dynamics is described in a mathematical framework similar to thermodynamics: the “evolution constant” k E and “evolutionary temperature” T evo play key roles similar to the Boltzmann constant k B and thermodynamic temperature T the , respectively. In the stationary state of the evolutionary dynamics, the attractor of the fitness is in inverse proportion to k E T evo . Furthermore, beyond the mathematical analogy, we obtained a biophysical connection between evolutionary dynamics and thermodynamics. Particularly, we found that T evo and T the are connected by k E T evo ≈ k B T the / 2 r . These results suggest that we can predict the fitness value in the stationary state by the thermodynamic temperature T the in the experimental setup.

New Mechanism for Positronium Formation on a Silicon Surface

We describe experiments in which positronium (Ps) is emitted from the surface of p-doped Si(100), following positron implantation. The observed emission rate is proportional to a Boltzmann factor exp{-E(A)/kT}, which is dependent on the temperature T of the sample and a characteristic energy E(A)=(0.253±0.004) eV. Surprisingly, however, the Ps emission energy has a constant value of ∼0.16 eV, much greater than kT. This observation suggests the spontaneous emission of energetic Ps from a short-lived metastable state that becomes thermally accessible to available surface electrons once the positron is present. A likely candidate for this entity is an electron-positron state analogous to the surface exciton observed on p-Si(100) c(4×2) by Weinelt et al. [Phys. Rev. Lett. 92, 126801 (2004)].

PERTURBATIVELY DEFINED EFFECTIVE CLASSICAL POTENTIAL IN CURVED SPACE

The partition function of a quantum statistical system in flat space can always be written as an integral over a classical Boltzmann factor exp [-βV eff cl (x0)], where V eff cl (x0) is the so-called effective classical potential containing the effects of all quantum fluctuations. The variable of integration is the temporal path average [Formula: see text]. We show how to generalize this concept to paths qμ(τ) in curved space with metric gμν(q), and calculate perturbatively the high-temperature expansion of V eff cl (q0). The requirement of independence under coordinate transformations qμ(τ)→ q′μ(τ) introduces subtleties in the definition and treatment of the path average [Formula: see text], and covariance is achieved only with the help of a suitable Faddeev–Popov procedure.

Andreev Reflection of Quasiparticles by a Vortex Tangle in Superfluid 3He-B?

We have made the surprising discovery that the thermal damping of a vibrating wire resonator in superfluid He-3-B at ultra low temperatures is considerably depressed when a second wire in the vicinity is driven supercritically. The damping of a vibrating wire resonator at low velocities in the B-phase arises from the scattering of quasiparticle excitations and has a temperature dependence proportional to the Boltzmann factor exp(-Delta /kT) at low temperatures. At higher velocities (v > v(L)/3), the wire breaks Cooper pairs and emits a quasiparticle beam. At first sight it seems paradoxical that heating the superfluid can reduce the quasiparticle flux: on a neighbouring wire. We can only understand this on the basis that vorticity emitted by the supercritical wire shields, via Andreev reflection, part of the background quasiparticle flux: from reaching the other wire. If this interpretation, is correct, these techniques will provide a sensitive probe of vortex dynamics in the ultra low temperature regime.

Molecular dynamics study of shear and tensile deformation of bicrystalline aluminum

This paper describes shear and tensile deformation of bicrystalline aluminum by computer molecular dynamics. A bicrystal model with a [001] (310) ∑=5 tilt grain boundary is used for simulations. The simulations show that the effect of temperature on both the shear and tensile deformation is represented by a Boltzmann factor exp (-Q/kBT) and that the deformation is thermally activated in a typical manner. We found that the activation energy Q for the high temperature range, where T is higher than approximately 500 K to 600 K, is significantly larger than that for the low temperature range. This result shows that there are different deformation mechanisms between high and low temperatures. The activation energy difference is considered to be caused by a structural transition at the grain boundary.

Superfluid 3He at very low temperatures: a very unusual excitation gas

The excitation gas in superfluid 3He at low temperatures shows a number of remarkable dynamical properties arising from the unusual dispersion curve. The existence of an energy gap leads to many of the observed properties varying rapidly with temperature, since the excitation density is dominated by the gap Boltzmann factor exp(—Δ/ kT). But also, the fact that the minimum energy lies at finite momentum gives rise to Andreev scattering processes, in which the velocity of the excitation is reversed but the momentum left virtually unchanged. Since the dispersion curve looks different to a moving observer, there is the possibility of the free production of quasiparticle-quasihole pairs at a Landau critical velocity. At low temperatures the mean free path becomes much larger than any experimental size. Using vibrating wire resonators as universal probes, we can monitor the temperature, measure the Kapitza resistance, examine the nonlinear regime beyond the two-fluid model, observe the Landau velocity, create and detect thermal beams of excitation with black-body radiators, observe Andreev reflection directly and probe A-phase textures (in which the gas is one-dimensional). Future possibilities are discussed.

Scalar field propagators in the microcanonical ensemble

The real-time thermal propagator of the canonical ensemble is shown to be the Laplace transform of a propagator which is an ensemble average over states with fixed energy E. This microcanonical propagator is temperature independent. The Boltzmann factor exp( − βE) in the Laplace transform produces the temperature dependence of the canonical thermal propagator. The singularity structure of the microcanonical propagator is investigated and an explicit perturbation calculation is performed in order to elucidate the origin of temperature-dependent masses.

Electroweak baryon number violation at finite temperature

We consider baryon and lepton number violating processes in the electroweak theory induced by gauge and Higgs fields passing the sphaleron solution at finite temperature. We show that for temperatures larger than 19 GeV the anomalous baryon and lepton number violating processes are suppressed by the Boltzmann factor exp (−βE sp), whereE sp is the sphaleron energy, rather than by the instanton tunneling factor exp (−8π2/g 2). We caculate the rate of baryon and lepton number violating processes at finite temperature and determine the freezing temperature of the anomalous processes in the early universe as a function of the Higgs mass. We compare the freezing temperature with the critical temperature of the electroweak phase transition infered from the one-loop finite-temperature effective potential. We obtain a critical Higgs mass of the order of 100 GeV, slightly depending on the top mass and the magnitude of the pre-exponential factor in the rate of theB non-conservation, above which the anomalous processes are certainly in equilibrium after the electroweak phase transition. Assuming that the temperature-dependence of the sphaleron energy is given by that found from the one-loop finitetemperature effective potential, this critical Higgs mass is lowered to a value of the order of 50 GeV.

Electron-hole pair mechanism for excitation of intramolecular vibrations in molecule-surface scattering

Abstract Recently excitation of the ν = 1 vibrational state of NO scattered from Ag(111) has been observed. The measured excitation probability goes as the Boltzmann factor exp ( −ℏomega; 0 k B T s ) where ω 0 is the vibration frequency and T S the surface temperature. We show that with reasonable assumptions the data can be explained by a mechanism in which vibrational excitation results from de-excitation of a hot electron-hole pair in the metal, the coupling to the molecular vibration being via electrons hopping in and out of the π ∗ orbital of NO. The “mechanical” mechanism is ruled out by the absence of excitation at low temperature.

Electron-hole pair mechanism for excitation of intramolecular vibrations in molecule-surface scattering

Recently excitation of the ν = 1 vibrational state of NO scattered from Ag(111) has been observed. The measured excitation probability goes as the Boltzmann factor exp( −ℏomega; 0 k B T s ) where ω 0 is the vibration frequency and T S the surface temperature. We show that with reasonable assumptions the data can be explained by a mechanism in which vibrational excitation results from de-excitation of a hot electron-hole pair in the metal, the coupling to the molecular vibration being via electrons hopping in and out of the π ∗ orbital of NO. The “mechanical” mechanism is ruled out by the absence of excitation at low temperature.

New Cluster Expansion Method in Lattice Gauge Theory

2) have been reported by many authors, and their results are very successful and give us values of various physical quantities such as the string tension and the mass gap. However, they are no more than numerical experiments. To understand the theory, we should have an explicit analytic expressions of these physical quantities. One method to get an analytic expression of them is the strong coupling expansion (S.C.E.).3) This expansion gives us a qualitative understanding of the lattice gauge theory. Especially the quark confinement and existence of the mass gap in the strong coupling limit are manifest in this expansion. The expansion series are convergent in the strong coupling region,4) and agreement between the Monte Carlo measurement and the strong coupling expansion series is very good in this region. But the series do not appear to be convergent in the weak coupling region, which we are interested in. Expansion parameter fl (inverse coupling constant squared) or u(fl) (coefficient of the fundamental representation in the character expansion of the Boltzmann factor exp(flS» used in this expansion is large or nearly equal to 1, respectively, in the

The determination of the effective rotational potential in the plastic phase of C2Cl6from neutron Bragg scattering data

The effective rotational potential V(ω) in the plastic phase of C2Cl6 is computed from neutron diffraction Bragg data. The formalism used applies the Boltzmann factor exp (- βV(ω)) in order to describe the orientational pair distribution function of the smeared nuclear scattering density. A model potential calculated from atom-atom interactions in an (8 + 1) cluster of molecules reproduces the potential V exp(ω) determined from the experiment fairly well. From this we conclude that V exp(ω) is due to the time independent crystalline potential rather than due to the averaged random rotational torque. The lowest rotational barrier height is approximately 1000 K.

Theory of defects in hard core statistical ensembles

Systems of particles are considered which interact only via their disk-shaped hard core. By use of the single occupancy model developed by Hoover and Ree we integrate out those degrees of freedom where the centers of particles are confined to “Wigner-Seitz” cells. In contrast to Hoover and Ree the auxiliary system of Wigner-Seitz cells is taken nonrigid and described by a set of vertex coordinates“η p”. The decimation procedure of degrees of freedom over the Wigner-Seitz cells leaves then the partition function defined in terms of the Boltzmann factor exp(δ S(“eta; p”)/ k B). Via the “interaction” function— Tδ S(“η p”) all the usual solid state properties are defined, e.g., elastic properties, phonon excitations and defects. This theory allows then a derivation of the positional correlation function which is done in the “harmonic” approximation for the solid and molten phase. The directional correlation function is discussed in terms of domains and their respective coincidence boundary system, and disclinations.

Conductance equation of dilute mixed strong electrolytes. III. Electrophoresis

The electrophoretic velocity is computed through the order linear in concentration for a system containing any number of species of ions of any charges. The computation is based on the general theory of Fuoss and Onsager and the method for the generalization to mixed electrolytes developed by Chen and Onsager for the primitive model. The Boltzmann factor exp. (—eiΨji/kT) is retained explicitly through the computation to obtain a result consistent with earlier computations of the relaxation field. The equilibrium potential including a correction to Poisson-Boltzmann equation is used, which adds a linear term ΔVjc to the electrophoretic velocity in agreement with the result of Murphy and Cohen. The correction to the ionic distribution due to the solvent motion is considered, which results in a linear term inversely proportional to the square of the viscosity of the solution. The main contribution is ΔVjE, which is in agreement with the result for symmetrical electrolytes of Falkenhagen et al. with only a slight difference due mainly to the different approximation used in the computation of the local force.

The Temperature Dependence of the Properties of Electrolyte Solutions. I. A Semi‐Phenomenological Approach to an Electrolyte Theory Including Short Range Forces

AbstractPair distribution functions f,ij(r1, r2) of a symmetrical ionophoric electrolyte compound Y Cz+ Az‐ in solution are determined with the help of a semi‐phenomenological method permitting to avoid a truncated series expansion of the Boltzmann factor exp [ — eo zj ψ i(r) k T] of Coulomb ion‐ion interaction in the vicinity of the i ion and to introduce the mean potential of short range forces. The appropriate chemical potential of the electrolyte component μY(p, T) and the relevant transport equations, especially of electrolyte conductance, are given. The concept of ion association is discussed within the framework of this approach.

Calculation of the positronium hyperfine pressure shift in buffer gases

An approximate quantitative theory of the positronium hyperfine pressure shift (HPS) is discussed. Adopting the approach of Adrian, the fractional shift Δ (R) is calculated as a function of the positronium–buffer gas separation R; the measured HPS is obtained by a thermal average of Δ (R) over R. A quantum mechanical averaging technique is used, rather than classical methods, in which the Boltzmann factor exp[−V (R)/kT], where V (R) is the intermolecular pair potential, is replaced by the positronium center-of-mass wavefunctions. The fractional shift Δ (R) is divided into two parts; a negative long range van der Waals contribution and a short range positive exchange contribution. It is argued that in the positronium center-of-mass approximation the short range contribution to Δ (R) is the same for both hydrogen and positronium and therefore existing calculations on hydrogen are utilized. Perturbation theory is used to obtain the long range contribution of Δ (R) and two models are used to evaluate the matrix elements that occur. In either model the long range contribution is related to the van der Waals interaction and can be obtained from a power series in R−1. A hard core potential model of the problem is solved exactly and predicts the HPS to be nearly temperature independent, a result essentially due to the long deBroglie wavelength of thermal positronium. Finally, the wave equation is numerically integrated with realistic potentials to find the positronium center-of-mass wavefunctions and the pressure shifts. Results of the numerical calculation also indicate a relatively small temperature coefficient of the HPS. The calculations of the positronium hyperfine pressure shift have substantially better agreement with measured pressure shifts than do calculations on hydrogen.

On Fluctuations of Temperature in Small Systems

Temperature is usually defined to be [(dS/dE)]−1. With a small system connected to a heat reservoir, there is a slight fluctuation of E, hence of the entropy S(E), hence of T. In this article it is shown that this definition implies that the average value of T is slightly higher than T0; however, the average of (1/T) is found to be (1/T0). It is also shown that the instantaneous Boltzmann factor exp(−E/kT) does not apply exactly to small systems, however, on the average, the Boltzmann factor exp(−E/kT0) does apply exactly.

EFFECTS OF ALCOHOLS ON ATOMIC-ABSORPTION AND EMISSION FLAME PHOTOMETRIC DETERMINATION OF SODIUM

在以Zeiss Ⅲ型火焰光度计改装成的装置上,以相同条件观察了不同浓度的甲醇、乙醇、丙醇对钠的原子吸收值及发射值的增强作用。测量了各种醇类、水溶液的表面张力及粘度,喷雾器的喷雾率及有效喷雾率,和火焰温度,并对醇类的增强作用的机理作了一些探讨。实验及计算结果表明,虽然有效喷雾率是决定吸收值增强作用的主要因素,但对于电离电位较低的碱金属,由于火焰温度降低而引起的电离度的减小亦起一定的作用,对于发射值的增强。除了有效喷雾率和电离度之外。还要考虑Boltznman因子e(Ei/kT)。