A new rigorous upper bound for the inverse critical temperature of the two-dimensional Coulomb gas

In this paper we show how to improve the recent result _c 17.2 on the inverse critical temperature for the two-dimensional Coulomb gas at low density to get the following upper bound: _c 16.     

Debye screening for two-dimensional Coulomb systems at high temperatures

The grand canonical ensemble of a two-dimensional Coulomb system with±1 charges is proved to have screening phenomena in its high-temperature region. The Coulomb potential in a finite region is assumed to be (–)^–1, where is the Laplacian with zero boundary conditions on. The hard-core condition is not assumed. The model is set up by separating (–)^–1 into a shortrange part and a long-range part depending on a parameter. The self-energies are subtracted only for the short-range part and therefore a choice of is a choice of subtraction of self-energies. The method of proof is in general the same as that of Brydges-Federbush Debye screening, except that here a modification for the short-range part of the potentials is needed.     

An analyticity bound for two-dimensional Ising model at low temperature

We study the coexistence phase in the two-dimensional Ising model. Optimizing the cluster expansion technique, we are able to prove the phase separation phenomenon, with the Onsager value for the surface tension, in a range , where estimates from above the critical within 19% and essentially coincides with the entropic bound.     

An upper bound for the ground-state energy of an antiferromagnetic chain with next-nearest-neighbor interaction

A trial function for the ground state of the antiferromagnetic linear chain leads to an equation for an upper bound of the ground-state energy per spin. This equation is solved exactly.     

An upper bound for the atomic ground state density at the nucleus

An upper bound on the atomic ground state density at the nucleus having the expectedZ ³ behavior as predicted by Lieb's Strong Scott Conjecture is proven.     

An upper bound for the adiabatic approximation error

In this paper,we derive an upper bound for the adiabatic approximation error,which is the distance between the exact solution to a Schr dinger equation and the adiabatic approximation solution.As an application,we obtain an upper bound for 1 minus the fidelity of the exact solution and the adiabatic approximation solution to a Schrdinger equation.     

An upper bound for the generalized adiabatic approximation error with a superposition initial state

The classical adiabatic approximation theory gives an adiabatic approximate solution to the Schr¨odinger equation(SE)by choosing a single eigenstate of the Hamiltonian as the initial state.The superposition principle of quantum states enables us to mathematically discuss the exact solution to the SE starting from a superposition of two different eigenstates of the time-dependent Hamiltonian H(0).Also,we can construct an approximate solution to the SE in terms of the corresponding instantaneous eigenstates of H(t).On the other hand,any physical experiment may bring errors so that the initial state(input state)may be a superposition of different eigenstates,not just at the desired eigenstate.In this paper,we consider the generalized adiabatic evolution of a quantum system starting from a superposition of two different eigenstates of the Hamiltonian at t=0.A generalized adiabatic approximate solution(GAAS)is constructed and an upper bound for the generalized adiabatic approximation error is given.As an application,the fidelity of the exact solution and the GAAS is estimated.     

Improved condition for the absence of bound states and converging analytic bounds to critical screening parameter

Converging lower bound to the critical screening parameterD _c associated with the ground state of a two-particle system interacting through a cut-off Coulomb potential is obtained analytically using an improved condition for the absence of bound states. The predicted numerical result for the lower bound is found to be within 10⁻³% of the exact result. On the other hand, a multi-parameter variational approach yields a tight upper bound, within 0.54% of the exact result. It is shown that the critical screening parameter for the exciteds-states can also be determined in an approximate way. We obtainD _c ^ms ≈ [0.764435n ⁻²+0.617737n ⁻³]⁻¹ wheren is the principal quantum number. The predictedD _c for various quantum states (n=1 to 8) are in good agreement with the values obtained numerically by Singh and Varshni.     

Sum rules for the one-component plasma with additional short-range forces

It is proved that, in the one-component plasma, with interactions including a non-Coulombic short-range part, the density derivative of the correlation functions _n (r ₁,,r _n) can be simply expressed as an integral of _n+1(r ₁,,r _n+1). This result is applied to prove the relation between the fourth moment of ₂ and the compressibility.     

An upper bound on the free energy for classical systems with Coulomb interactions in a varying external field

The thermodynamic limit is taken using a sequence of regions all the same shape as a given region of volume ||, with a specified distribution of normal field component on . We show that with magnetostatic interactions the limiting free energy density is bounded above by jhen where (,B) is the free energy density for a system of density in a uniform external fieldB and the inf is taken over all divergence-free fieldsB with given normal component on and all densities (x) compatible with particle number constraints of the form where _i is a sub-region of . A physical argument suggests that this upper bound is the true thermodynamic limit, and that it takes account demagnetization effects. Electrostatic interactions can be treated similarly.     

An iterated Mayer expansion for the Yukawa gas

We construct a convergent expansion for the Yukawa gas at small activity and inverse temperature < 4/e ².Research partially supported by Ministero della Pubblica Istruzione and CNR-GNFM.     

Lower and upper bounds on the critical temperature for anisotropic three-dimensional Ising model

The Ising model is considered on a simple cubic lattice, with a coupling constant J along one axis and coupling constants J’ along the remaining two axes. The transfer-matrix technique and an extended phenomenological renormalization group theory [18, 19] are applied to obtain two-sided bounds on the critical temperature for the model with J′/J≤1. The bounds monotonically converge with decreasing J′/J and provide improved estimates for the phase-transition temperature in anisotropic three-dimensional Ising model, as compared with those available from the literature.     

On the critical temperature of a superconducting system

Based on the assumption that in the groundbcs state the net gain in energy is equivalent to the repulsive electron-ion and electron-electron Darwin interactions, an expression forT _c has been obtained which depends on only a few atomic parameters. The theory provides a criterion for the occurrence of superconductivity and yields satisfactory values ofT _c for metals and alloys, and ternary chalcogenides and borides. It explains the difference inT _c in the crystalline and amorphous states as well as the pressure dependence ofT _c . The possibility of occurrence of high temperature superconductivity has been explored.     

Analyticity and Mixing Properties for Random Cluster Model with q >0 on ℤ d

We study the Random Cluster Model on ℤ ^d for p near either 0 or 1 and for all q > 0 and we prove by mean of cluster expansion methods the analyticity of the pressure and finite connectivities in both regimes. These results are valid also in the regime q < 1 and they imply that percolation probability is strictly less than 1.     

An exponential upper bound for the survival probability in a dynamic random trap model

We consider a symmetric translation-invariant random walk on thed-dimensional lattice ? ^d . The walker moves in an environment of moving traps. When the walker hits a trap, he is killed. The configuration of traps in the course of time is a reversible Markov process satisfying a level-2 large-deviation principle. Under some restrictions on the entropy function, we prove an exponential upper bound for the survival probability, i.e., $$\mathop {lim sup}\limits_{t \to \infty } \frac{1}{t}\log \mathbb{P}(T \geqslant t)< 0$$ whereT is the survival time of the walker. As an example, our results apply to a random walk in an environment of traps that perform a simple symmetric exclusion process.     

Generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of scatterers

We presesent an exact generalization of the Foldy-Lax formula for the self-energy of a wave propagating in a disordered system of identical spherical scatterers. The Foldy-Lax formula yields an expression for the self-energy valid to first order in the density of scatterers. Our exact formula allows a systematic calculation of corrections to this low-density approximation. The formula is based on a renormalized cluster expansion which was presented earlier.     

Correlations equalities and some upper bounds for the critical temperature for spin one systems

Starting from correlation identities for the Blume–Capel spin 1 systems and using correlation inequalities, we obtain rigorous upper bounds for the critical temperature. The obtained results improve over effective field type results.     

A renormalized equation for the three-body system with short-range interactions

We study the three-body system with short-range interactions characterized by an unnaturally large two-body scattering length. We show that the off-shell scattering amplitude is cutoff independent up to power corrections. This allows us to derive an exact renormalization group equation for the three-body force. We also obtain a renormalized equation for the off-shell scattering amplitude. This equation is invariant under discrete scale transformations. The periodicity of the spectrum of bound states originally observed by Efimov is a consequence of this symmetry. The functional dependence of the three-body scattering length on the two-body scattering length can be obtained analytically using the asymptotic solution to the integral equation. An analogous formula for the three-body recombination coefficient is also obtained.     

Effects of the upper level coupling field on lasing without inversion in a V-type system

Driven by one upper level coupling field, a three-level V-type atomic system with a pair of upper levels is studied. With one strong coupling field and one weak probe field, it is found that, due to the effects of the upper level coupling field, the quantum coherence between the two upper levels can be induced, and the absorption of the probing field is very sensitive to the relative phase of the probe, the pumping and the upper level coupling fields. With proper parameters, lasing without inversion (LWI) can be realized.     

制冷系统连续融霜过程中制冷温度变化规律的研究

连续融霜是一种在除霜过程中制冷不间断、库温上升小、无需附加能耗的除霜方式。为探究在不同工况下除霜时,连续融霜系统制冷剂进出口温度、库温波动及融霜时间的变化规律,在库温-18、-12℃两种工况下,对冷风机制冷剂进出口温度、库温、融霜时间及融霜能耗进行测量分析。结果表明:库温-18℃,制冷风机微压差计示数在17 Pa时比在60 Pa融霜时的库温波动值和融霜时间分别减少0.8℃、200 s,融霜能耗降低9.03%;库温-12℃,制冷风机微压差计示数在17 Pa比在40 Pa融霜时的库温波动和融霜时间分别减少2℃、284 s,融霜能耗降低53.3%。因此,融霜时制冷风机霜层厚度对库温、融霜时间及融霜能耗有一定影响。