@article { author = {S. Azakov, and N. Heydari,}, title = {Path Integral Methods for Single Band Hubbard Model}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {71-85}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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.}, keywords = {}, title_fa = {روش انتگرال مسیر برای مدل ‌هابارد تک نواره}, abstract_fa = {  در این مقاله طرق مختلفی که تاکنون با استفاده از روش انتگرال مسیر برای بررسی مدل هابارد تک نواره به کار رفته است, مرور می­شود. تأکید این مقاله بر نحوه نوشتن کنش برای انتگرال مسیر است و در باره نتایجی که از این فرمولبندیها به دست می­آید, کمتر بحث می­شود.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1503.html}, eprint = {https://ijpr.iut.ac.ir/article_1503_11c16ec23383d89c8c22eee2aa748997.pdf} } @article { author = {G. A. Parsafar, and K. K. Darani,}, title = {Monte Carlo Simulation of the (100) Surface of the fcc Lattice of Platinum and Gold}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {86-93}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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.}, keywords = {}, title_fa = {شبیه سازی سطح (100) شبکه fcc پلاتین و طلا به روش مونت-کارلو}, abstract_fa = {  با استفاده از روش مونت ـ کارلو سطح (100) شبکه مکعبی مرکز سطحی فلزات طلا و پلاتین شبیه سازی شده است. معادله پتانسیلی که برای توصیف رفتار اتمهای تشکیل دهنده این سطوح مورد استفاده قرار گرفته, پتانسیل ساتن و چن است. این تابع پتانسیل اختصاصاً برای سیستمهای متشکل از هسته­های غوطه­ور در دریای الکترونی طراحی شده است که در آن انرژی پتانسیل هر اتم به چگالی الکترونی محیطی بستگی دارد که در آن قرار گرفته است. همین بستگی, این معادله را در زمره پتانسیلهای بس ذره­ای قرار می­دهد.   با افزایش دما, اتمهای سازنده سطح به موقعیتهای خالی روی سطح منتقل می­شوند. این جابه­جاییها منجر به افزایش تعداد ناراستیها, افزایش سطح شبکه و تغییر عدد کوئوردینانسیون می­شود. در هر انتقال, فقط یک گام, یعنی انتقال به نزدیکترین موقعیت خالی مجاور مجاز است و همین باعث می­شود که سیستم در یک حالت جدید انرژی قرار بگیرد. حرکتهای اولیه منجر به افت و خیزهای شدیدی در انرژی سیستم می­شود ولی با گذشت مدت زمان نسبتاً طولانی, یعنی هنگامی که تعداد گامها از مرتبه چند صدهزار شود, تغییرات انرژی سیستم به ازای یک گام خیلی جزئی خواهد شد و با تقریب بسیار خوبی می­توان از افت و خیز در انرژی چشم پوشید و آرایش حاصل را به عنوان حالت پایدار سیستم در دمای مورد بررسی در نظر گرفت. در این محاسبات, برهم کنش هر ذره با اولین و دومین همسایه نزدیک آن در نظر گرفته می­شود و انتقالهایی پذیرفته می­شوند که انرژی آنها با توجه به ضریب بولتزمن مناسب باشد. در نهایت اندازه سطح را به صورت تابعی از دما به دست آوردیم. نتایج محاسبات نشان می­دهند که وقتی قسمتی از سطح از اتم خالی می­شود, سایر انتقالها عمدتاً طوری صورت می­گیرند که اندازه این حفره بزرگ شود. جهت حصول اطمینان از صحت عملیات شبیه سازی, از معادله شوتکی استفاده شد؛ به این ترتیب که خطی بودن لگاریتم طبیعی نسبت تعداد نقصهای ایجاد شده به کل تعداد اتمها بر حسب معکوس دما مورد تأیید قرار گرفت.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1504.html}, eprint = {https://ijpr.iut.ac.ir/article_1504_1be7b2541e5cf835b9ca87df692ae8a5.pdf} } @article { author = {M. T. Tavassoli, and A. Doroudi,}, title = {Reconstruction of Interfering Waves from Three Dimensional Analysis of Their Interference Pattern}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {94-102}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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.}, keywords = {}, title_fa = {بازسازی دو سطح موج با استفاده از تحلیل نقش تداخلی آنها در سه بعد}, abstract_fa = {  در این کار به طور نظری و تجربی نشان داده می­شود که تا تحلیل نقش تداخلی دو سطح موج نامشخص در سه بعد سطحهای موج را می­توان مشخص کرد.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1505.html}, eprint = {https://ijpr.iut.ac.ir/article_1505_e69ca4cbac746812deddea5729bd69d5.pdf} } @article { author = {J. Ghanbari, and A. Khesali,}, title = {A Model for the Dynamical and Ionization Structure of Planetary Nebula IC 418}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {103-109}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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}, keywords = {}, title_fa = {مدلی برای ساختار دینامیکی و یونیدگی سحابی سیاره نمای (418 IC)}, abstract_fa = {  با ارائه مدل دو باد ستاره­ای و یک تابع توزیع چگالی وابسته به عکس مجذور فاصله, ساختار دینامیکی ویونیدگی سحابی سیاره نمای 418 IC را مطالعه کردیم. باد سریعی با انرژی مکانیکی  2/34×1034erg.s-1 با  ابربادی با آهنگ جرمی  2×10-5M(°)yr-1و سرعت 10 کیلومتر بر ثانیه برخورد می­کند, و محیط متراکم درخشانی را به وجود می­آورد. در این مدل, سرعت انبساط خطوط طیفی OI برابر با 11 کیلومتر بر ثانیه, و برای خطوط طیفی HI برابر با 5/10 کیلومتر بر ثانیه پیش بینی می­شود. عمر دینامیکی 1033 سال برای سحابی توافق خوبی با عمر تحولی ستاره بعد از برخورد دو باد ستاره­ای دارد, که به درخشندگی  (°)1125L برای ستاره مرکزی, و جرم(°) 0/05M  برای سحابی منجر می­شود.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1506.html}, eprint = {https://ijpr.iut.ac.ir/article_1506_47813bba771a2ddc840b8e4889a3aa37.pdf} } @article { author = {M. t. Tavassoli, and H. r. Khalesi Fard,}, title = {Nonlinear Refractive Index Measurement in Semiconductor-Doped Glasses}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {110-118}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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.}, keywords = {}, title_fa = {اندازه‌گیری ضریب شکست غیر خطی در شیشه‌های آلاییده به بلورهای نیمرسانا}, abstract_fa = {  در این مقاله با استفاده از آزمایش پمپ ـ کاوه, با دو روش جدید, ضریب شکست غیر خطی شیشه­های GG550 اندازه­گیری شده است. این شیشه­ها از نوع شیشه­های آلاییده به بلورهای نیمرسانا هستند. اساس اندازه­گیری, تحلیل نقش تداخلی موجهای بازتابیده کاوه از دو سطح تیغه نمونه است که توسط باریکه پمپ تحریر می­شوند.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1507.html}, eprint = {https://ijpr.iut.ac.ir/article_1507_ddd46762c71a369e2510889d830eb8c7.pdf} } @article { author = {B. S. Sabzevari,}, title = {Four-Dimensional Propagation and Coupling of Electromagnetic Waves in Inhomogenous Anisotropic Non-Stationary Absorbing Media}, journal = {Iranian Journal of Physics Research}, volume = {1}, number = {2}, pages = {119-139}, year = {2020}, publisher = {Isfahan University of Technology, The Physics Society of Iran}, issn = {1682-6957}, eissn = {2345-3664}, doi = {}, abstract = {  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.}, keywords = {}, title_fa = {انتشار و جفت شدن امواج الکترومغناطیسی چهار بعدی در محیطهای ناهمگن، ناهمسانگرد، ناساکن و جاذب}, abstract_fa = {  در این مقاله یک توصیف کامل چهاربعدی خطی برای انتشار و جفت شدن امواج الکترومغناطیسی در کلیترین حالت محیط, یعنی در محیطهایی که در همه جهات فضای سه بعدی ناهمگن و از نظر زمانی ناساکن و در ضمن ناهمسانگرد و جاذب نیز هستند ارائه می­شود. تنها شرط, کندی تغییر خواص خود محیط (مانند چگالی و غیره) است. معادلات دیفرانسیل برای امواج در هر دو حالت انتشار تکی و جفت شدن ارائه و در امتداد مسیرهای موج حل شده­اند.}, keywords_fa = {}, url = {https://ijpr.iut.ac.ir/article_1508.html}, eprint = {https://ijpr.iut.ac.ir/article_1508_9136bc4c4525a1edbe0d2214182c2a5a.pdf} }