Concept of time in the general law of thermodynamics as the basis of the thermodynamics of the nonequilibrium state

A mathematical formulation is proposed for the general law of thermodynamics in the form of relations defining the concept of thermodynamic time and the criterion of stable equilibrium. It is hypothesized that an implicit function F(, , , , ... ⁽ⁿ⁾)=0 associates the thermodynamic time and the potential of the nonequilibrium state. Partial solutions of a general form are also obtained for the trajectories of a nonequilibrium process, characterized by the presence of only one independent variable, i.e., =(⁽ⁿ⁾).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 49–54, August, 1989.     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

More surprises in the general theory of lattice systems

I use Israel's methods to prove new theorems of ubiquitous pathology for classical and quantum lattice systems. The main result is the following: Let be any interaction and be any translation-invariant equilibrium state for (extremal or not). Then there exists a sequence { _k } of interactions converging to , having extremal (or even unique) translation-invariant equilibrium states _k , such that { _k } converges to . In certain situations the perturbations _k – can be chosen to lie in a cone of antiferromagnetic pair interactions. I discuss the connection with results of Daniëls and van Enter, and point out an application to the one-dimensional ferromagnetic Ising model with 1/r ² interaction (Thouless effect).     

Currents and Super-Operator Product Expansionsof N = 4 Super-W Algebra

The currents and the super-operators product expansions of theN = 4 super-Walgebra are obtained. The generators of this extended conformal algebra consistof the stress-tensor superfield J and the primary superfields _±v ^q of integer orhalf-integer conformal weight and Cartan–Weylcharge q. The algorithm forderiving the N = 4 super-W algebra is given for particular cases. Explicit formsof the operator product algebra for different values of are given.     

On the domains of generalized operators

The domains of generalized operatorsT: _–+ on rigged Hilbert spaces _– H ₊ are investigated. We introduce an equivalence relation for operators with different domains. Arguments are given for taking ₊ to be the weak quasi-completion of _– and for _– to be Mackey quasi-complete. For domains of closed symmetric Hilbert space operators we give a representation for ₊ and provide certain elements in the equivalence class of the corresponding operator.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

Bianchi and Weyl equations as sufficient equations for Einstein spaces

When the Bianchi equation and the wave equation for the Weyl spinor are written in the form which they take for Einstein spaces, but with the symmetric 4-spinor _ABCD considered arbitrary and with the background space unspecified, ^EA _EBCD=0; (+12) _ABCD –6(AB ^EF ( _CD )EF =0 it is shown that — in general — for this pair of equations to be consistent, the background space has to be an Einstein space, and the symmetric 4-spinor _ABCD has to be the Weyl spinor of this space.     

Ground state and lowest eigenvalue of the Laplacian for non-compact hyperbolic surfaces

LetM be a complete Riemannian surface with constant curvature –1, infinite volume, and a finitely generated fundamental group. Denote by (M) the lowest eigenvalue of the Laplacian onM, and let _M be the associated eigenfunction. We estimate the size of (M) and the shape of _M by a finite procedure which has an electrical circuit analogue. Using the Margulis lemma, we decomposeM into its thick and thin parts. On the compact thick components, we show that _M varies from a constant value by no more thanO( ). The estimate for (M) is calculable in terms of the topology ofM and the lengths of short geodesics ofM. An analogous theorem of the compact case was treated in [SWY].     

Ergodic properties of infinite-dimensional stochastic systems

The ergodic properties of two stochastic models _I and _II are investigated. Each model is described by a fieldx(t),t > 0, on the lattice =Z ^d,d < . For _I,x(t) evolves according to the equations wherex _s (t) R for eachs eF. Here the {w_s(t): s } are independent, one-dimensional Wiener processes, ₂ is a bounded interaction between adjacent lattice sites, and the potentials ₁ and ₂ satisfy appropriate regularity conditions. It is shown that for each model,x(t) is a Markov process on an infinite-dimensional phase spaceX. The probability measures onX that satisfy the Dobrushin-Lanford-Ruelle (DLR) conditions are stationary for this process and have a mixing property. Moreover, for _I any stationary, time-reversal-invariant probability measure that has certain regularity properties must satisfy the DLR conditions.This paper is based on a portion of the author's Ph.D. thesis.⁽²⁾     

Parametric dependence of the properties of pulsed-laser-deposited diamond-like carbon films

The properties of Pulsed-Laser-Deposited Diamond-Like Carbon (PLD DLC) films are studied as functions of the power density and the wavelength of the laser beam, and the incident angle of the beam relative to the normal of the target surface. All the films have a similar structure consisting of graphite particulates embedded in a continuous matrix, so the macroscopic performance of the films is determined by the overall contributions of the particulates and the matrix. The use of higher, shorter, or larger leads to an enhancement of the diamond-like characteristics and a simultaneous increase of the particulate density. These two effects give opposite contributions to the electrical conductivity _R, leading to the following results. (i) _R drops with increasing in the low range (region I) due to the stronger diamond-like nature of the matrix, but increases sharply after has exceeded a threshold _min as a result of the rapid increase in particulate density. (ii) In region I, the use of shorter or larger leads to a more diamond-like matrix, and this overwhelms the degradation effect caused by the slight increase in particulate density. The samples thus become more insulating. In the high region (region II), however, the use of shorter or larger gives rise to higher particulate density, thereby increasing the electrical conductivity.     

Conserved moments in nonequilibrium field dynamics

We demonstrate with the example of Cahn-Hilliard dynamics that the macroscopic kinetics of first-order phase transitions exhibits an infinite number of constants of motion. Moreover, this result holds in any space dimension for a broad class of nonequilibrium processes whose macroscopic behavior is governed by equations of the form /t = W(), where is an order parameter,W is an arbitrary function of , and is a linear Hermitian operator. We speculate on the implications of this result.     

The translation-rotation paradox in the nucleation theory

The factor of 10¹⁷ proposed by Lothe and Pound in the theory of nucleation of droplets from the vapor phase is studied using classical statistical mechanics. The controversial factor is derived from partition functions for an isolatedn-mer and for ann-molecular cluster imbedded in the bulk liquid phase. The rotational degrees of freedom have no place in, in agreement with Reiss, Katz, and Cohen's treatment. It is proved that the surface free energy of a cluster is proportional to the surface area. The estimate of what Lothe and Pound called the replacement term is different from those of previous authors. It is concluded that is written as a ratio = _g/_l, where _g and _l , are the volumes per molecule in the gas phase and in the liquid phase, respectively. For water at 300K, is approximately equal to 10₄.     

Thermodynamics of a dense self-avoiding walk with contact interactions

A lattice model is used to study the properties of an infinite self-avoiding linear polymer chain that occupies a fraction, 01, of sites on ad-dimensional hypercubic lattice. The model introduces an (attractive or repulsive) interaction energy between nonbonded monomers that are nearest neighbors on the lattice. The lattice cluster theory enables us to derive a double series expansion in and d^–1 for the chain free energy per segment while retaining the full dependence. Thermodynamic quantities, such as the entropy, energy, and mean number of contacts per segment, are evaluated, and their dependences on, , andd are discussed. The results are in good accordance with known limiting cases.     

The hydrodynamic limit of a one-dimensional nearest neighbor gradient system

We study the hydrodynamic behavior of a one-dimensional nearest neighbor gradient system with respect to a positive convex potential . In the hydrodynamic limit the density distribution is shown to evolve according to the nonlinear diffusion equation ,(q)/t= (²/dq²){F([1/₁(q)]), with F= –.     

Supersymmetric path integrals applied to the transmission of a mesoscopic ring

The average transmission probability of a one-dimensional mesoscopic ring is calculated for arbitrary disorder strength. With increasing disorder the dependence on the magnetic flux changes from ₀ to ₀/2 periodicity. A supersymmetric method is used for the calculation which leads to the quantum mechanics in super-space of an anharmonic oscillator with hyperbolic symmetry. As a byproduct the transmission of a mesoscopic wire is obtained. The inverse of the localization length is given by the lowest eigenvalue of the oscillator.Research performed within the program of Sonderforschungsbereich 341 Köln-Aachen-Jülich     

A Note on the Time Development of Quantum Lattice Systems

The time development of quantum lattice systems is studied without any restrictions on the growth condition of the potential . A thermodynamic limit of quantum Gibbs state, a *-algebra and an automorphism group _t for which is a KMS state are constructed.     

Interacting spinor and scalar fields: Exact self-consistent solutions in Bianci I space

Exact self-consistent solutions of the equations that describe a system of interacting spinor and massless scalar fields with the interaction Lagrangian L_int=_,^,(S), where (S) is an arbitrary function of the invariant S=, are obtained in Bianci I space. The possibility of excluding the initial singularity is studied for the case of a power-law function (S), and isotropic expansion of the space as t is established.Russian University of International Amity. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–58, July, 1995.     

Treatment of droplike clusters in nucleation theory using Reiss's method

The expression of the correction factor in nucleation theory is derived by extending the method Reiss used recently. is the factor appearing in the number of critical nuclei (formed as a vapor condenses into liquid drops) as a correction to the conventional theory. It is shown that=p _l / _g /kT, wherep _l is the pressure of the liquid phase inside the drop, _g , is the volume per molecule in the vapor phase,k is the Boltzmann constant, andT is the absolute temperature. The difference between this and Reiss's expression isp _l , which replaces hisp _g (the vapor pressure in equilibrium with the drop). The derived in this paper is compatible with the expression= _g / _l ( _l is the molecular volume in the liquid phase) previously proposed by the present author.     

Streuung spinpolarisierter Elektronen an Au(110)

Using the the spin modulated polarized electron gun based on photoemission from positive affinity GaAs the intensityI(E, , ) and asymmetry (E, , ) are measured in LEED from Au(110). The asymmetry is compared with the polarizationS(E, , ) which N. Müller obtained with a Mott detector after scattering an unpolarized electron beam from the same crystal. There is excellent agreement for the (00) beams, if the scattering plane is a mirror symmetry plane of the crystal (=0°, =90°). From the differences for the (00) and (11) beams at =35° and the (01/2) beam at =90° conditions for possible models for the reconstructed Au(110)–(1×2) surface may be derived.

---

---

Die vorliegende Arbeit ist ein Auszug aus [1]

---

Neue Addresse ab 1. Oktober 1980: B. Reihl, IBM Thomas J. Watson Research Center, Yorktown Heights, NY 10598, USA     

Tunable UV radiation at short wavelengths (188–240 nm) generated by sum-frequency mixing in lithium borate

Sum-frequency mixing (₃=₁+₂) of UV laser radiation (₁=266 nm and 213 nm) and tunable coherent infrared light (₂=1.2–2.6 m) in lithium borate (LBO) generates radiation at short wavelengths (₃=188–242 nm). The UV radiation at ₁ is produced by the fourth and fifth harmonic of a pulsed Nd-YAG laser. The infrared light is generated with an optical parametric oscillator of beta barium borate. The phase-matching angle is measured as function of ₃ and compared with calculated values. For UV laser radiation at shorter wavelengths (173 nm₁213 nm) the calculations predict an extension of the tuning range of the sum-frequency generated at ₃ to wavelengths as short as the LBO transmission cutoff at 160 nm.