Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
Path Integral Methods for Single Band Hubbard Model
Path Integral Methods for Single Band Hubbard Model
71
85
1503
FA
S. Azakov
N. Heydari
Journal Article
2020
02
02
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorphic representions the partition function of the model can be straightforwardly expressed as a path integral with respect to Grassmann fields. Then the question arises how to calculate this path integral specially in the most interesting case of the strong coupling, which is described by the term quartic in the fermion fields. The standard way to get rid of this quartic term is to use so-called Hubbard-Stratonovich transformation by introducing auxilary boson field (this procedure is usually called bosonization). Since there are several equivalent forms of the interaction term in the single-band Hubbard model the bosonization procedure is not unique. In the first section of the article we discuss two types of bosoniztions one with two real scalar fields (charge and spin fields) and another with a real vector field. The second section is devoted to a spin-rotation-invariant bosonization procedure invented by Schulz and Weng, Ting and Lee, where an arbitary quantization axis is introduced at each point in space and time and an integration over all possible orientations enters the path integral measure. Spin rotation invariant formulation is necessary to study e.g. spiral magnetization. In the third section we present the contstruction of a path integral for the partition function when the single-band Hubbard Hamiltonian is written in terms of the Hubbard operators, which are elements of the doubly graded semi-simple algebra. In this case one should use generalized coherent states for superalgebra in order to get a path integral formulation. We follow the procedure proposed recently by T ngler and Kopp, to investigate the case of strong coupling.
We review various ways to express the partition function of the single-band Hubard model as a path integral. The emphasis is made on the derivation of the action in the integrand of the path integral and the results obtained from this approach are discussed only briefly. Since the single-band Hubbard model is a pure fermionic model on the lattice and its Hamiltonian is a polynomial in creation and annihilation fermionic operators, with the help of the fermionic coherent states of holomorphic representions the partition function of the model can be straightforwardly expressed as a path integral with respect to Grassmann fields. Then the question arises how to calculate this path integral specially in the most interesting case of the strong coupling, which is described by the term quartic in the fermion fields. The standard way to get rid of this quartic term is to use so-called Hubbard-Stratonovich transformation by introducing auxilary boson field (this procedure is usually called bosonization). Since there are several equivalent forms of the interaction term in the single-band Hubbard model the bosonization procedure is not unique. In the first section of the article we discuss two types of bosoniztions one with two real scalar fields (charge and spin fields) and another with a real vector field. The second section is devoted to a spin-rotation-invariant bosonization procedure invented by Schulz and Weng, Ting and Lee, where an arbitary quantization axis is introduced at each point in space and time and an integration over all possible orientations enters the path integral measure. Spin rotation invariant formulation is necessary to study e.g. spiral magnetization. In the third section we present the contstruction of a path integral for the partition function when the single-band Hubbard Hamiltonian is written in terms of the Hubbard operators, which are elements of the doubly graded semi-simple algebra. In this case one should use generalized coherent states for superalgebra in order to get a path integral formulation. We follow the procedure proposed recently by T ngler and Kopp, to investigate the case of strong coupling.
https://ijpr.iut.ac.ir/article_1503_11c16ec23383d89c8c22eee2aa748997.pdf
Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
Monte Carlo Simulation of the (100) Surface of the fcc Lattice of Platinum and Gold
Monte Carlo Simulation of the (100) Surface of the fcc Lattice of Platinum and Gold
86
93
1504
FA
G. A. Parsafar
K. K. Darani
Journal Article
2020
02
02
In this work, the (100) surface of Au and Pts face centered cubic lattice, has been simulated in Monte-Carlo method, using a 486-DX2 computer. The potential equation that was used for the interaction among atoms in the metal surfaces is called Sutton and Chen potential. This potential is introduced for the interaction of floating nuclei in the electron sea, and attractive term is a many body potential. Surface atoms are allowed to move to their adjacent unoccupied sites. These movements occur when temperature increases by which surface configuration, coordination number and the solid surface will be changed. In primary movements, we have large flactuations for the energy, but when the number of movements become large enough (order of hunders of thouands), we may ignore the small energy flactuation and therefore stable configuration can obtained. In this calculation, we have taken into account the interaction between any particle with its first and second neighbouring atoms. Probability of acceptance of any movement is equal to the Boltzman factor. Finally, an equation, that is temperature dependency of surface magnitude, was abtained.
In this work, the (100) surface of Au and Pts face centered cubic lattice, has been simulated in Monte-Carlo method, using a 486-DX2 computer. The potential equation that was used for the interaction among atoms in the metal surfaces is called Sutton and Chen potential. This potential is introduced for the interaction of floating nuclei in the electron sea, and attractive term is a many body potential. Surface atoms are allowed to move to their adjacent unoccupied sites. These movements occur when temperature increases by which surface configuration, coordination number and the solid surface will be changed. In primary movements, we have large flactuations for the energy, but when the number of movements become large enough (order of hunders of thouands), we may ignore the small energy flactuation and therefore stable configuration can obtained. In this calculation, we have taken into account the interaction between any particle with its first and second neighbouring atoms. Probability of acceptance of any movement is equal to the Boltzman factor. Finally, an equation, that is temperature dependency of surface magnitude, was abtained.
https://ijpr.iut.ac.ir/article_1504_1be7b2541e5cf835b9ca87df692ae8a5.pdf
Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
Reconstruction of Interfering Waves from Three Dimensional Analysis of Their Interference Pattern
Reconstruction of Interfering Waves from Three Dimensional Analysis of Their Interference Pattern
94
102
1505
FA
M. T. Tavassoli
A. Doroudi
Journal Article
2020
02
02
Optical interferometry is being used as an efficient tool to analyse smooth surfaces for more than a century. Although, due to introduction of novel computer assisted analyzing techniques and array detectors, like CCD, the speed and the precision of processing have been increased tremendously, but the main equation involved is not changed. The main equation is the intensity distribution in the interference pattern of a plane reference wave and the required wave. In the paper it is shown that by analysis of the interference pattern of two unknown waves in three dimension (which is possible for coherent waves) it is possible to reconstruct each wave separately. This approach has several useful applications, namely, on can do without reference plane wave in the interferometric surface analysis and, it is possible to reconstruct an unknown wave by making it to interfere with itself. This is very useful in determining the profile of laser beams and erasing the effect of atmospheric disturbances on observing astronomical objects.
Optical interferometry is being used as an efficient tool to analyse smooth surfaces for more than a century. Although, due to introduction of novel computer assisted analyzing techniques and array detectors, like CCD, the speed and the precision of processing have been increased tremendously, but the main equation involved is not changed. The main equation is the intensity distribution in the interference pattern of a plane reference wave and the required wave. In the paper it is shown that by analysis of the interference pattern of two unknown waves in three dimension (which is possible for coherent waves) it is possible to reconstruct each wave separately. This approach has several useful applications, namely, on can do without reference plane wave in the interferometric surface analysis and, it is possible to reconstruct an unknown wave by making it to interfere with itself. This is very useful in determining the profile of laser beams and erasing the effect of atmospheric disturbances on observing astronomical objects.
https://ijpr.iut.ac.ir/article_1505_e69ca4cbac746812deddea5729bd69d5.pdf
Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
A Model for the Dynamical and Ionization Structure of Planetary Nebula IC 418
A Model for the Dynamical and Ionization Structure of Planetary Nebula IC 418
103
109
1506
FA
J. Ghanbari
A. Khesali
Journal Article
2020
02
02
The interacting two winds model and a spherical density distribution function are introduced to study the dynamical and ionization structure of the planetary nebula IC 418. A fast wind with a mechanical luminousity 2/34×1034erg.s-1 of interacts with a super wind with a mass-loss rate of 2×10-5M(°)yr-1 and a velocity of 10 , and produces a dense and luminous medium. In this model, the expansion velocities of OI and HI lines are predicted to be 11 and 10.5kms-1 , respectively. The calculated dynamical time-scale 1033yr for the nebula is in good agreement with the evolution time of the central star after the interaction of the two winds. Our calculations give a luminosity 0.05M(°)of for the central star
The interacting two winds model and a spherical density distribution function are introduced to study the dynamical and ionization structure of the planetary nebula IC 418. A fast wind with a mechanical luminousity 2/34×1034erg.s-1 of interacts with a super wind with a mass-loss rate of 2×10-5M(°)yr-1 and a velocity of 10 , and produces a dense and luminous medium. In this model, the expansion velocities of OI and HI lines are predicted to be 11 and 10.5kms-1 , respectively. The calculated dynamical time-scale 1033yr for the nebula is in good agreement with the evolution time of the central star after the interaction of the two winds. Our calculations give a luminosity 0.05M(°)of for the central star
https://ijpr.iut.ac.ir/article_1506_47813bba771a2ddc840b8e4889a3aa37.pdf
Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
Nonlinear Refractive Index Measurement in Semiconductor-Doped Glasses
Nonlinear Refractive Index Measurement in Semiconductor-Doped Glasses
110
118
1507
FA
M. T. Tavassoli
H. R. Khalesi Fard
Journal Article
2020
02
02
There are several techniques in use for non-linear refractive index measurement, namely, interferometric techniques, in which conventional inter-ferometers are used, degenerate for wave mixing (DFWM), and z-scan, Each of these techniques suffers from some shortcmings. For example conventional interferometers like Fabry-Perot and Twyman-Green need high quality optical components, unwanted reflections on these components produce noise, and the device limits the probe-pump anglc, or in z-scan technique one needs very sensitive detectors and since the intensity is monitored by the nonlinear absorption, which is usually present, reduces the measurement accuracy. In the techniqucs introduced here, in principle, only a plate of the sample is required, and even parallelism of the plate surfaces is not curcial. Experiments can be carried out successfully if the angle between the plate surface is less than few minutes. In the first technique, the probe beam strikes the surface at an arbitray angle of incidence. The reflected beam from the two surfaces of the sample interfere on a photo-sensitive screen like CCD, and more or less linear interference fringes are produced. When the pump beam is switched on, the interference pattern deforms. The amount and the direction of the deformation give the value and the sign of the non-linear refractive index. In this technique the probe-pump angle can be varied from 00 to 1900. In the second technique, interference between the reflected probe beam from the sample and the diffracted pump beam from the grating induced by the interference of the probe and the pump beams, leads to a series of circular fringes. When the non-linear sample is replaced by a linear material like fuse silica glass, the above mentioned circular fringes are formed, but the number of fringes in a specified angular interval remains fixed as the pump beam intensity increases. But, in the case of a non-linear sample the number changes due to self focusing or defocusing induced by pump beam. The curvature of diffracted wave is deduced from the measurement of the radii of circular fringes for different pump intensities and this leads to the evaluation of non-linear refractive index. It is shown that an accuracy of π/10 in measuring the phase of the diffracted spherical wave front, leads to an accuracy of 5% in measurement of nonlinear retractive index. Bout techniques have been carried out using the second harmonic of a Nd,YAG laser with 8ns pulse duration, and the samples were Schotts OG550 filters of 1mm thickness. The exeperimental results of both techniques are in agreement with each other and with the results of the other reports.
There are several techniques in use for non-linear refractive index measurement, namely, interferometric techniques, in which conventional inter-ferometers are used, degenerate for wave mixing (DFWM), and z-scan, Each of these techniques suffers from some shortcmings. For example conventional interferometers like Fabry-Perot and Twyman-Green need high quality optical components, unwanted reflections on these components produce noise, and the device limits the probe-pump anglc, or in z-scan technique one needs very sensitive detectors and since the intensity is monitored by the nonlinear absorption, which is usually present, reduces the measurement accuracy. In the techniqucs introduced here, in principle, only a plate of the sample is required, and even parallelism of the plate surfaces is not curcial. Experiments can be carried out successfully if the angle between the plate surface is less than few minutes. In the first technique, the probe beam strikes the surface at an arbitray angle of incidence. The reflected beam from the two surfaces of the sample interfere on a photo-sensitive screen like CCD, and more or less linear interference fringes are produced. When the pump beam is switched on, the interference pattern deforms. The amount and the direction of the deformation give the value and the sign of the non-linear refractive index. In this technique the probe-pump angle can be varied from 00 to 1900. In the second technique, interference between the reflected probe beam from the sample and the diffracted pump beam from the grating induced by the interference of the probe and the pump beams, leads to a series of circular fringes. When the non-linear sample is replaced by a linear material like fuse silica glass, the above mentioned circular fringes are formed, but the number of fringes in a specified angular interval remains fixed as the pump beam intensity increases. But, in the case of a non-linear sample the number changes due to self focusing or defocusing induced by pump beam. The curvature of diffracted wave is deduced from the measurement of the radii of circular fringes for different pump intensities and this leads to the evaluation of non-linear refractive index. It is shown that an accuracy of π/10 in measuring the phase of the diffracted spherical wave front, leads to an accuracy of 5% in measurement of nonlinear retractive index. Bout techniques have been carried out using the second harmonic of a Nd,YAG laser with 8ns pulse duration, and the samples were Schotts OG550 filters of 1mm thickness. The exeperimental results of both techniques are in agreement with each other and with the results of the other reports.
https://ijpr.iut.ac.ir/article_1507_ddd46762c71a369e2510889d830eb8c7.pdf
Isfahan University of Technology,
The Physics Society of Iran
Iranian Journal of Physics Research
1682-6957
1
2
2020
02
02
Four-Dimensional Propagation and Coupling of Electromagnetic Waves in Inhomogenous Anisotropic Non-Stationary Absorbing Media
Four-Dimensional Propagation and Coupling of Electromagnetic Waves in Inhomogenous Anisotropic Non-Stationary Absorbing Media
119
139
1508
FA
B. S. Sabzevari
Journal Article
2020
02
02
A complete linear theory in four dimensional space-time is constructed for propagation and coupling of electromagnetic waves in the most general case, i.e. media where all three space directions are in homogeneous and where temporal changes, anisotropy and absorbtion are also included. The only condition is that the properties of the medium should be slowly varying, Although it is assumed that absorption may be strong. The differential equations for the waves are analytically solved for both individual propagation of the waves and coupling of two waves.
A complete linear theory in four dimensional space-time is constructed for propagation and coupling of electromagnetic waves in the most general case, i.e. media where all three space directions are in homogeneous and where temporal changes, anisotropy and absorbtion are also included. The only condition is that the properties of the medium should be slowly varying, Although it is assumed that absorption may be strong. The differential equations for the waves are analytically solved for both individual propagation of the waves and coupling of two waves.
https://ijpr.iut.ac.ir/article_1508_9136bc4c4525a1edbe0d2214182c2a5a.pdf