Effect of Quantum Statistics

Another way to describe this situation is to remember that in perfect gases Bose-Einstein statistics gives rise to an apparent short-range attraction and Fermi-Dirac statistics to an apparent short-range repulsion (cf. Hirschfelder, Curtiss and Bird [1954]). These apparent interactions are probably partially destroyed by the short-range repulsive forces. For this reason the statistical effect is somewhat reduced. The physical picture of the state of liquid helium at 0 K would be the following we have a more or less regular distribution of particles in which each atom tends to remain separate from the 

There remains a large entropy in liquid He at the lowest temperatures investigated, which can certainly not be explained merely by the difference in mass between He and He . 

The atonoic nature of the excitations both in liquid He and He , is at present very uncertain and we shall not go into details. The most promisLog lines of approach seem to be, at present, the consideration of simple possible trial functions, for the wave function as suggested by Feynman [1954, 1955] as well as the consideration of multiple cdl occupations which permit the introduction of the effects of statistics (Prigogine and Phxlippot [1952,1953], De Boer and Cohen [1955]). 

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Many interesting quantum effects appear at low temperatures due to the effect of quantum statistics. Very interesting PIMC studies of such effects have been done for structural phase transitions in adsorbed " He and He layers [90-91] and for the superfluidity of H2 layers [92]. For studies of related systems and additional information see Sec. IV D 2. 

Although we have explained Bose-Einstein condensation as a characteristic of an ideal or nearly ideal gas, i.e., a system of non-interacting or weakly interacting particles, systems of strongly interacting bosons also undergo similar transitions. Eiquid helium-4, as an example, has a phase transition at 2.18 K and below that temperature exhibits very unusual behavior. The properties of helium-4 at and near this phase transition correlate with those of an ideal Bose-Einstein gas at and near its condensation temperature. Although the actual behavior of helium-4 is due to a combination of the effects of quantum statistics and interparticle forces, its qualitative behavior is related to Bose-Einstein condensation. 

Increasing the purity of organic crystals and reducing the contact resistance in OFETs is another challenging direction of future experimental work, which will help to extend the temperature range where the intrinsic polaronic transport can be studied. The development of more advanced techniques for purification of molecular materials will enable the expansion of the intrinsic transport regime to much lower temperatures, where the effects of quantum statistics and polaron-polaron interactions should become experimentally accessible. 

Cell Model 385. 5. Effect of Quantum Statistics 389. 6. Isotope Effect and... 

The leading correction to the classical ideal gas pressure temi due to quantum statistics is proportional to 1 and to n. The correction at constant density is larger in magnitude at lower temperatures and lighter mass. The coefficient of can be viewed as an effective second virial coefficient The effect of quantum... 

For the PIMC study of quantum statistics effects in He systems and additional references see Refs. 90, 91. 

Beyond the clusters, to microscopically model a reaction in solution, we need to include a very big number of solvent molecules in the system to represent the bulk. The problem stems from the fact that it is computationally impossible, with our current capabilities, to locate the transition state structure of the reaction on the complete quantum mechanical potential energy hypersurface, if all the degrees of freedom are explicitly included. Moreover, the effect of thermal statistical averaging should be incorporated. Then, classical mechanical computer simulation techniques (Monte Carlo or Molecular Dynamics) appear to be the most suitable procedures to attack the above problems. In short, and applied to the computer simulation of chemical reactions in solution, the Monte Carlo [18-21] technique is a numerical method in the frame of the classical Statistical Mechanics, which allows to generate a set of system configurations... 

Role of quantum statistics. When considering complex systems by methods of statistical physics, one operates with their time-dependent distributions. In fermionic systems (see Yu. Ozhigov), statistical requirements imply that we must replace the independent-particle description by a quasiparticle formalism for quantum information processing. Effects of statistical fluctuations on coherent scattering processes (see M. Blaauboer et al.) suggest the need for furher exploration of the role of statistics on the dynamics of entangled systems. 

The path integral formulation of quantum statistical mechanics has become a powerful technique for describing quantum effects in liquids. " Path integrals introduce an effective quantum correction to the classical interaction potential. The classical two-body potential between two atoms of mass ntj and with coordinates x, and Xy is replaced by an effective potential between two ring polymers, each held together by a harmonic nearest-neighbor interaction,... 

The computation of quantum many-body effects requires additional effort compared to classical cases. This holds in particular if strong collective phenomena such as phase transitions are considered. The path integral approach to critical phenomena allows the computation of collective phenomena at constant temperature — a condition which is preferred experimentally. Due to the link of path integrals to the partition function in statistical physics, methods from the latter — such as Monte Carlo simulation techniques — can be used for efficient computation of quantum effects. 

Permutations of this type have to be considered in PIMC simulations if a full account of the quantum statistics is intended in the study and required by the physical effect under consideration, which means that additional permutation moves have to be done in the simulation. In this way quantum statistics has been included in a few PIMC simulations, in particular for the study of superfluidity in He [287] and in adsorbed H2 layers [92], for the Bose-Einstein condensation of hard spheres [269], and for the analysis of... 

Where A F(z) is the free energy at z relative to that at the reactant state minimum zr, and the ensemble average < > is obtained by a quantum mechanical effective potential [15]. Note that the inherent nature of quantum mechanics is at odds with a potential of mean force as a function of a finite reaction coordinate. Nevertheless, the reaction coordinate function z[r] can be evaluated from the path centroids r, first recognized by Feynman and Flibbs as the most classical-like variable in quantum statistical mechanics and later explored by many researchers [14, 15]. 

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