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Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions 具有伽马、对数正态和 F 分布的狄拉克振荡器的超统计特性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040111
S. Siouane, A. Boumali, A. Guvendi
{"title":"Superstatistical properties of the Dirac oscillator with gamma, lognormal, and F distributions","authors":"S. Siouane,&nbsp;A. Boumali,&nbsp;A. Guvendi","doi":"10.1134/S0040577924040111","DOIUrl":"10.1134/S0040577924040111","url":null,"abstract":"<p> We explore the thermal characteristics of fermionic fields with a nonminimal coupling in one, two, and three dimensions using the framework of superstatistics theory. We consider three distinct distributions: the gamma distribution, the lognormal distribution, and the F distribution. Each of these distributions is governed by a specific probability density function. To calculate the partition function, we use the Euler–Maclaurin formula, specifically in the low-energy asymptotic approximation of superstatistics. This calculation takes the remainder term into consideration. In each scenario, using the derived partition functions, we analyze the variations in entropy and specific heat with varying temperatures and the universal parameter denoted as <span>(q)</span>. In general, we observe that increasing the value of <span>(q)</span> enhances all the curves. Additionally, we note that entropy values tend to increase as the temperature decreases, and tend to decrease as the parameter <span>(q)</span> increases. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800543","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Yang–Baxter equation in all dimensions and universal qudit gates 所有维度的杨-巴克斯特方程和通用奎特门
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-04-26 DOI: 10.1134/S0040577924040032
A. Pourkia
{"title":"Yang–Baxter equation in all dimensions and universal qudit gates","authors":"A. Pourkia","doi":"10.1134/S0040577924040032","DOIUrl":"10.1134/S0040577924040032","url":null,"abstract":"<p> We construct solutions of the Yang–Baxter equation in any dimension <span>(dge 2)</span> by directly generalizing the previously found solutions for <span>(d=2)</span>. We equip those solutions with unitarity and entangling properties. Being unitary, they can be turned into <span>(2)</span>-qudit quantum logic gates for qudit-based systems. The entangling property enables each of those solutions, together with all <span>(1)</span>-qudit gates, to form a universal set of quantum logic gates. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140800618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Motion of particles in the field of nonlinear wave packets in a liquid layer under an ice cover 冰盖下液层中非线性波包场中的粒子运动
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030097
A. T. Il’ichev, A. S. Savin, A. Yu. Shashkov
{"title":"Motion of particles in the field of nonlinear wave packets in a liquid layer under an ice cover","authors":"A. T. Il’ichev,&nbsp;A. S. Savin,&nbsp;A. Yu. Shashkov","doi":"10.1134/S0040577924030097","DOIUrl":"10.1134/S0040577924030097","url":null,"abstract":"<p> We consider a liquid layer of a finite depth described by Euler’s equations. The ice cover is geometrically modeled by a nonlinear elastic Kirchhoff–Love plate. We determine the trajectories of liquid particles under an ice cover in the field of a nonlinear surface traveling wave rapidly decaying at infinity, namely, a solitary wave packet (a monochromatic wave under the envelope, with the wave velocity equal to the envelope velocity) of a small but finite amplitude. Our analysis is based on the use of explicit asymptotic expressions for solutions describing the wave structures at the water–ice interface of a solitary wave packet type, as well as asymptotic solutions for the velocity field generated by these waves in the depth of the liquid. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
One-parameter discrete-time Calogero–Moser system 单参数离散时间卡洛吉罗-莫泽系统
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030012
U. Jairuk, S. Yoo-Kong
{"title":"One-parameter discrete-time Calogero–Moser system","authors":"U. Jairuk,&nbsp;S. Yoo-Kong","doi":"10.1134/S0040577924030012","DOIUrl":"10.1134/S0040577924030012","url":null,"abstract":"<p> We present a new type of integrable one-dimensional many-body systems called a one-parameter Calogero–Moser system. At the discrete level, the Lax pairs with a parameter are introduced and the discrete-time equations of motion are obtained as together with the corresponding discrete-time Lagrangian. The integrability property of this new system can be expressed in terms of the discrete Lagrangian closure relation by using a connection with the temporal Lax matrices of the discrete-time Ruijsenaars–Schneider system, an exact solution, and the existence of a classical <span>(r)</span>-matrix. As the parameter tends to zero, the standard Calogero–Moser system is recovered in both discrete-time and continuous-time forms. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Evolution of the magnetic field in spatially inhomogeneous axion structures 空间不均匀轴心结构中的磁场演变
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030103
M. S. Dvornikov, P. M. Akhmet’ev
{"title":"Evolution of the magnetic field in spatially inhomogeneous axion structures","authors":"M. S. Dvornikov,&nbsp;P. M. Akhmet’ev","doi":"10.1134/S0040577924030103","DOIUrl":"10.1134/S0040577924030103","url":null,"abstract":"<p> We study the time evolution of magnetic fields in various configurations of spatially inhomogeneous pseudoscalar fields that are a coherent superposition of axions. For such systems, we derive a new induction equation for the magnetic field, which takes this inhomogeneity into account. Based on this equation, we study the evolution of a pair of Chern–Simons waves interacting with a linearly decreasing pseudoscalar field. The nonzero gradient of the pseudoscalar field leads to the mixing of these waves. We then consider the problem in a compact domain in the case where the initial Chern–Simons wave is mirror symmetric. The pseudoscalar field inhomogeneity then leads to an effective change in the <span>(alpha)</span> dynamo parameter. Thus, the influence of a spatially inhomogeneous pseudoscalar field on the magnetic field evolution bears a strong dependence on the system geometry. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198534","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Quantifying the irreversibility of channels 量化通道的不可逆转性
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S004057792403005X
Shunlong Luo, Yuan Sun
{"title":"Quantifying the irreversibility of channels","authors":"Shunlong Luo,&nbsp;Yuan Sun","doi":"10.1134/S004057792403005X","DOIUrl":"10.1134/S004057792403005X","url":null,"abstract":"<p> In contrast to unitary evolutions, which are reversible, generic quantum processes (operations and quantum channels) are often irreversible. However, the degree of irreversibility is different for different channels, and it is desirable to have a quantitative characterization of irreversibility. In this paper, by exploiting the channel–state duality implemented by the Jamiołkowski–Choi isomorphism, we quantify the irreversibility of channels via entropy of the Jamiołkowski–Choi states of the corresponding channels and compare it with the notions of entanglement fidelity and entropy exchange. General properties of a reasonable measure of irreversibility are discussed from an intuitive perspective, and entropic measures of irreversibility are introduced. Several relations between irreversibility, entanglement fidelity, the degree of nonunitality, and decorrelating power are established. Some measures of irreversibility for a variety of prototypical channels are evaluated explicitly, revealing some information-theoretic aspects of the structure of channels from the perspective of irreversibility. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Digital representation of continuous observables in quantum mechanics 量子力学中连续观测值的数字表示
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030073
M. G. Ivanov, A. Yu. Polushkin
{"title":"Digital representation of continuous observables in quantum mechanics","authors":"M. G. Ivanov,&nbsp;A. Yu. Polushkin","doi":"10.1134/S0040577924030073","DOIUrl":"10.1134/S0040577924030073","url":null,"abstract":"<p> To simulate quantum systems on classical or quantum computers, the continuous observables (e.g., coordinate and momentum or energy and time) must be reduced to discrete ones. In this paper, we consider the continuous observables represented in the positional systems as power series in the radix multiplied over the summands (“digits”), which turn out to be Hermitian operators with discrete spectrum. We investigate the obtained quantum mechanical operators of digits, the commutation relations between them, and the effects of the choice of a numeral system on lattices and representations. Renormalizations of diverging sums naturally occur in constructing the digital representation. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Causal perturbative QED and white noise 因果微扰 QED 和白噪声
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030085
J. Wawrzycki
{"title":"Causal perturbative QED and white noise","authors":"J. Wawrzycki","doi":"10.1134/S0040577924030085","DOIUrl":"10.1134/S0040577924030085","url":null,"abstract":"<p> We present Bogoliubov’s causal perturbative QFT with only one refinement: the creation–annihilation operators at a point, i.e., for a specific momentum, are mathematically interpreted as the Hida operators from the white noise analysis. We leave the rest of the theory completely unchanged. This allows avoiding infrared (and ultraviolet) divergences in the transition to the adiabatic limit for interacting fields and eliminating the free parameters of the theory associated with the choice of normalization in computation of the retarded and advanced parts of causal distributions (corresponding to the freedom in choosing the renormalization scheme). This enhances the predictive power of the theory, and in particular allows deriving nontrivial mass relations. The approach is general and can be applied to investigate any perturbative QFT. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation 惠瑟姆调制理论和广田失焦方程周期解下的溃坝问题
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030036
Xinyue Li, Qian Bai, Qiulan Zhao
{"title":"Whitham modulation theory and dam-breaking problem under periodic solutions to the defocusing Hirota equation","authors":"Xinyue Li,&nbsp;Qian Bai,&nbsp;Qiulan Zhao","doi":"10.1134/S0040577924030036","DOIUrl":"10.1134/S0040577924030036","url":null,"abstract":"<p> We explore the Whitham modulation theory and one of its physical applications, the dam-breaking problem for the defocusing Hirota equation that describes the propagation of ultrashort pulses in optical fibers with third-order dispersion and self-steepening higher-order effects. By using the finite-gap integration approach, we deduce periodic solutions of the equation and discuss the degeneration of genus-one periodic solution to a soliton solution. Furthermore, the corresponding Whitham equations based on Riemann invariants are obtained, which can be used to modulate the periodic solutions with step-like initial data. These Whitham equations with the weak dispersion limit are quasilinear hyperbolic equations and elucidate the averaged dynamics of the fast oscillations referred to as dispersive shocks, which occur in the solution of the defocusing Hirota equation. We analyze the case where both characteristic velocities in genus-zero Whitham equations are equal to zero and the values of two Riemann invariants are taken as the critical case. Then by varying these two values as step-like initial data, we study the rarefaction wave and dispersive shock wave solutions of the Whitham equations. Under certain step-like initial data, the point where two genus-one dispersive shock waves begin to collide at a certain time, that is, the point where the genus-two dispersive shock wave appears, is investigated. We also discuss the dam-breaking problem as an important physical application of the Whitham modulation theory. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the factorization method for the quantum statistical description of dynamics of an isolated spin system 论孤立自旋系统动力学量子统计描述的因式分解法
IF 1 4区 物理与天体物理
Theoretical and Mathematical Physics Pub Date : 2024-03-22 DOI: 10.1134/S0040577924030061
A. A. Samokhin, A. V. Zyl, N. L. Zamarashkin
{"title":"On the factorization method for the quantum statistical description of dynamics of an isolated spin system","authors":"A. A. Samokhin,&nbsp;A. V. Zyl,&nbsp;N. L. Zamarashkin","doi":"10.1134/S0040577924030061","DOIUrl":"10.1134/S0040577924030061","url":null,"abstract":"<p> We study the applicability of the formula that factors the trace of the diagonal part of spin operator products in the case of a relatively small number of particles of an isolated spin system. The validity of this formula for a large number of particles follows from the basic principles of quantum statistical mechanics. The spin system under consideration includes dipole–dipole interaction and the Zeeman interaction with an external magnetic field. We establish that the accuracy of this formula monotonically increases as the magnetic field increases. At the same time, the dependence on the number of particles in the range <span>(2div10)</span> for various configurations turns out to be sharply nonmonotone. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140198458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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