Phy5670/QLG: Difference between revisions
SuvadipDas (talk | contribs) (New page: ==Introduction== A lattice model first proposed in 1956 has been introduced to explain the peculiar properties and phase transitions in liquid helium.In this model, the liquid is regarded...) |
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A lattice model first proposed in 1956 has been introduced to explain the peculiar properties and phase transitions in liquid helium.In this model, the liquid is regarded as a lattice composed of atoms and holes, where each atom can migrate by exchanging its position with an adjacent hole.The kinetic and potential energies are defined in terms of creation and annihilation operators for the atom sin each lattice site such that they boil down to the appropriate form in the limit of vanishing lattice spacing.An analogy has been drawn between the lattice liquid and a system of vector spins subjected to an external magnetic field, with identification of corresponding physical quantities.Finally,the quantum lattice gas model has been implemented to describe essential aspects of the motion of <math>^{4}\textrm{He}</math> atoms and of <math>^{3}\textrm{He}</math> impurities in solid <math>^{4}\textrm{He}</math>.The study suggested the affinity of <math>^{3}\textrm{He}</math> impurities to bind to defects and promote <math>^{4}\textrm{He}</math> atoms to interstitial sites which can turn the bosonic quantum disordered crystal into a metastable supersolid.It is further proposed that such defects can form a glass phase during the <math>^{4}\textrm{He}</math> solid growth by rapid cooling. | A lattice model first proposed in 1956 has been introduced to explain the peculiar properties and phase transitions in liquid helium.In this model, the liquid is regarded as a lattice composed of atoms and holes, where each atom can migrate by exchanging its position with an adjacent hole.The kinetic and potential energies are defined in terms of creation and annihilation operators for the atom sin each lattice site such that they boil down to the appropriate form in the limit of vanishing lattice spacing.An analogy has been drawn between the lattice liquid and a system of vector spins subjected to an external magnetic field, with identification of corresponding physical quantities.Finally,the quantum lattice gas model has been implemented to describe essential aspects of the motion of <math>^{4}\textrm{He}</math> atoms and of <math>^{3}\textrm{He}</math> impurities in solid <math>^{4}\textrm{He}</math>.The study suggested the affinity of <math>^{3}\textrm{He}</math> impurities to bind to defects and promote <math>^{4}\textrm{He}</math> atoms to interstitial sites which can turn the bosonic quantum disordered crystal into a metastable supersolid.It is further proposed that such defects can form a glass phase during the <math>^{4}\textrm{He}</math> solid growth by rapid cooling. | ||
===The Lattice Gas Model=== | |||
The lattice model for classical liquid is well known for providing an adequate approximation for the purpose of taking into consideration the large atomic correlation in liquid phase.Each atom is assumed to occupy only discrete lattice points and the configurations of liquid are described by the distributions of atoms and holes among the lattice points.By choosing a proper magnitude of lattice constant, and excluding the multiple occupation of atoms on each lattice point, one can account for the effect of the strong repulsion between atoms. | |||
Revision as of 20:03, 5 December 2010
Introduction
A lattice model first proposed in 1956 has been introduced to explain the peculiar properties and phase transitions in liquid helium.In this model, the liquid is regarded as a lattice composed of atoms and holes, where each atom can migrate by exchanging its position with an adjacent hole.The kinetic and potential energies are defined in terms of creation and annihilation operators for the atom sin each lattice site such that they boil down to the appropriate form in the limit of vanishing lattice spacing.An analogy has been drawn between the lattice liquid and a system of vector spins subjected to an external magnetic field, with identification of corresponding physical quantities.Finally,the quantum lattice gas model has been implemented to describe essential aspects of the motion of atoms and of impurities in solid .The study suggested the affinity of impurities to bind to defects and promote atoms to interstitial sites which can turn the bosonic quantum disordered crystal into a metastable supersolid.It is further proposed that such defects can form a glass phase during the solid growth by rapid cooling.
The Lattice Gas Model
The lattice model for classical liquid is well known for providing an adequate approximation for the purpose of taking into consideration the large atomic correlation in liquid phase.Each atom is assumed to occupy only discrete lattice points and the configurations of liquid are described by the distributions of atoms and holes among the lattice points.By choosing a proper magnitude of lattice constant, and excluding the multiple occupation of atoms on each lattice point, one can account for the effect of the strong repulsion between atoms.