Pub Date : 2024-03-01DOI: 10.1134/s004057792403005x
Abstract
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.
{"title":"Quantifying the irreversibility of channels","authors":"","doi":"10.1134/s004057792403005x","DOIUrl":"https://doi.org/10.1134/s004057792403005x","url":null,"abstract":"<span> <h3>Abstract</h3> <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> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-01","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}
Pub Date : 2024-03-01DOI: 10.1134/s0040577924030085
Abstract
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.
{"title":"Causal perturbative QED and white noise","authors":"","doi":"10.1134/s0040577924030085","DOIUrl":"https://doi.org/10.1134/s0040577924030085","url":null,"abstract":"<span> <h3>Abstract</h3> <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> </span>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-01","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020053
T. V. Dudnikova
Abstract
We consider the Cauchy problem for the Hamiltonian system consisting of the Klein–Gordon field and an infinite harmonic crystal. The dynamics of the coupled system is translation-invariant with respect to the discrete subgroup (mathbb{Z}^d) of (mathbb{R}^d). The initial date is assumed to be a random function that is close to two spatially homogeneous (with respect to the subgroup (mathbb{Z}^d)) processes when (pm x_1>a) with some (a>0). We study the distribution (mu_t) of the solution at time (tinmathbb{R}) and prove the weak convergence of (mu_t) to a Gaussian measure (mu_infty) as (ttoinfty). Moreover, we prove the convergence of the correlation functions to a limit and derive the explicit formulas for the covariance of the limit measure (mu_infty). We give an application to Gibbs measures.
{"title":"Stabilization of the statistical solutions for large times for a harmonic lattice coupled to a Klein–Gordon field","authors":"T. V. Dudnikova","doi":"10.1134/s0040577924020053","DOIUrl":"https://doi.org/10.1134/s0040577924020053","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the Cauchy problem for the Hamiltonian system consisting of the Klein–Gordon field and an infinite harmonic crystal. The dynamics of the coupled system is translation-invariant with respect to the discrete subgroup <span>(mathbb{Z}^d)</span> of <span>(mathbb{R}^d)</span>. The initial date is assumed to be a random function that is close to two spatially homogeneous (with respect to the subgroup <span>(mathbb{Z}^d)</span>) processes when <span>(pm x_1>a)</span> with some <span>(a>0)</span>. We study the distribution <span>(mu_t)</span> of the solution at time <span>(tinmathbb{R})</span> and prove the weak convergence of <span>(mu_t)</span> to a Gaussian measure <span>(mu_infty)</span> as <span>(ttoinfty)</span>. Moreover, we prove the convergence of the correlation functions to a limit and derive the explicit formulas for the covariance of the limit measure <span>(mu_infty)</span>. We give an application to Gibbs measures. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987868","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020107
Z. Korichi, A. Souigat, R. Bekhouche, M. T. Meftah
Abstract
We solve the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives for systems exhibiting noninteger power laws in their Hamiltonians. Based on the fractional Liouville equation, we calculate the density function (DF) of a classical ideal gas. If the Riemann–Liouville derivative is used, the DF is a function depending on both the momentum (p) and the coordinate (q), but if the derivative in the Caputo sense is used, the DF is a constant independent of (p) and (q). We also study a gas consisting of (N) fractional oscillators in one-dimensional space and obtain that the DF of the system depends on the type of the derivative.
{"title":"Solution of the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives in statistical mechanics","authors":"Z. Korichi, A. Souigat, R. Bekhouche, M. T. Meftah","doi":"10.1134/s0040577924020107","DOIUrl":"https://doi.org/10.1134/s0040577924020107","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We solve the fractional Liouville equation by using Riemann–Liouville and Caputo derivatives for systems exhibiting noninteger power laws in their Hamiltonians. Based on the fractional Liouville equation, we calculate the density function (DF) of a classical ideal gas. If the Riemann–Liouville derivative is used, the DF is a function depending on both the momentum <span>(p)</span> and the coordinate <span>(q)</span>, but if the derivative in the Caputo sense is used, the DF is a constant independent of <span>(p)</span> and <span>(q)</span>. We also study a gas consisting of <span>(N)</span> fractional oscillators in one-dimensional space and obtain that the DF of the system depends on the type of the derivative. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987873","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020089
K. Khachnaoui
Abstract
We investigate a particular type of damped vibration systems that incorporate impulsive effects. The objective is to establish the existence and multiplicity of (Q)-rotating periodic solutions. To achieve this, the variational method and the fountain theorem, as presented by Bartsch, are used. The research builds upon recent findings and extends them by introducing notable enhancements.
{"title":"Infinitely many rotating periodic solutions for damped vibration systems","authors":"K. Khachnaoui","doi":"10.1134/s0040577924020089","DOIUrl":"https://doi.org/10.1134/s0040577924020089","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We investigate a particular type of damped vibration systems that incorporate impulsive effects. The objective is to establish the existence and multiplicity of <span>(Q)</span>-rotating periodic solutions. To achieve this, the variational method and the fountain theorem, as presented by Bartsch, are used. The research builds upon recent findings and extends them by introducing notable enhancements. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987869","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020065
M. O. Katanaev
Abstract
On (pseudo)Riemannian manifolds of two and three dimensions, we list all metrics that admit a complete separation of variables in the Hamilton–Jacobi equation for geodesics. There are three different classes of separable metrics on two-dimensional surfaces. Three-dimensional manifolds admit six classes of separable metrics. Within each class, metrics are related by canonical transformations and a nondegenerate transformation of parameters that does not depend on coordinates.
{"title":"Separation of variables in the Hamilton–Jacobi equation for geodesics in two and three dimensions","authors":"M. O. Katanaev","doi":"10.1134/s0040577924020065","DOIUrl":"https://doi.org/10.1134/s0040577924020065","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> On (pseudo)Riemannian manifolds of two and three dimensions, we list all metrics that admit a complete separation of variables in the Hamilton–Jacobi equation for geodesics. There are three different classes of separable metrics on two-dimensional surfaces. Three-dimensional manifolds admit six classes of separable metrics. Within each class, metrics are related by canonical transformations and a nondegenerate transformation of parameters that does not depend on coordinates. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139988020","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020016
A. Aksentijević, S. Aleksić, S. Pilipović
Abstract
We analyze shift-invariant spaces (V_s), subspaces of Sobolev spaces (H^s(mathbb{R}^n)), (sinmathbb{R}), generated by a set of generators (varphi_i), (iin I), with (I) at most countable, by the use of range functions and characterize Bessel sequences, frames, and the Riesz basis of such spaces. We also describe (V_s) in terms of Gramians and their direct sum decompositions. We show that (finmathcal D_{L^2}'(mathbb{R}^n)) belongs to (V_s) if and only if its Fourier transform has the form (hat f=sum_{iin I}f_ig_i), (f_i=hatvarphi_iin L_s^2(mathbb{R}^n)), ({varphi_i(,cdot+k)colon kinmathbb Z^n,,iin I}) is a frame, and (g_i=sum_{kinmathbb{Z}^n}a_k^ie^{-2pisqrt{-1},langle,{cdot},,krangle}), with ((a^i_k)_{kinmathbb{Z}^n}inell^2(mathbb{Z}^n)). Moreover, connecting two different approaches to shift-invariant spaces (V_s) and (mathcal V^2_s), (s>0), under the assumption that a finite number of generators belongs to (H^scap L^2_s), we give the characterization of elements in (V_s) through the expansions with coefficients in (ell_s^2(mathbb{Z}^n)). The corresponding assertion holds for the intersections of such spaces and their duals in the case where the generators are elements of (mathcal S(mathbb R^n)). We then show that (bigcap_{s>0}V_s) is the space consisting of functions whose Fourier transforms equal products of functions in (mathcal S(mathbb R^n)) and periodic smooth functions. The appropriate assertion is obtained for (bigcup_{s>0}V_{-s}).
{"title":"The structure of shift-invariant subspaces of Sobolev spaces","authors":"A. Aksentijević, S. Aleksić, S. Pilipović","doi":"10.1134/s0040577924020016","DOIUrl":"https://doi.org/10.1134/s0040577924020016","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We analyze shift-invariant spaces <span>(V_s)</span>, subspaces of Sobolev spaces <span>(H^s(mathbb{R}^n))</span>, <span>(sinmathbb{R})</span>, generated by a set of generators <span>(varphi_i)</span>, <span>(iin I)</span>, with <span>(I)</span> at most countable, by the use of range functions and characterize Bessel sequences, frames, and the Riesz basis of such spaces. We also describe <span>(V_s)</span> in terms of Gramians and their direct sum decompositions. We show that <span>(finmathcal D_{L^2}'(mathbb{R}^n))</span> belongs to <span>(V_s)</span> if and only if its Fourier transform has the form <span>(hat f=sum_{iin I}f_ig_i)</span>, <span>(f_i=hatvarphi_iin L_s^2(mathbb{R}^n))</span>, <span>({varphi_i(,cdot+k)colon kinmathbb Z^n,,iin I})</span> is a frame, and <span>(g_i=sum_{kinmathbb{Z}^n}a_k^ie^{-2pisqrt{-1},langle,{cdot},,krangle})</span>, with <span>((a^i_k)_{kinmathbb{Z}^n}inell^2(mathbb{Z}^n))</span>. Moreover, connecting two different approaches to shift-invariant spaces <span>(V_s)</span> and <span>(mathcal V^2_s)</span>, <span>(s>0)</span>, under the assumption that a finite number of generators belongs to <span>(H^scap L^2_s)</span>, we give the characterization of elements in <span>(V_s)</span> through the expansions with coefficients in <span>(ell_s^2(mathbb{Z}^n))</span>. The corresponding assertion holds for the intersections of such spaces and their duals in the case where the generators are elements of <span>(mathcal S(mathbb R^n))</span>. We then show that <span>(bigcap_{s>0}V_s)</span> is the space consisting of functions whose Fourier transforms equal products of functions in <span>(mathcal S(mathbb R^n))</span> and periodic smooth functions. The appropriate assertion is obtained for <span>(bigcup_{s>0}V_{-s})</span>. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987876","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020028
I. Ya. Aref’eva, I. V. Volovich
Abstract
Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of their entropy. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in (D = 4) space–time dimensions is provided by the analytic continuation of the entropy of Bose gas with a nonrelativistic one-particle energy to (d =-4) negative spatial dimensions. In this paper, we show that the (D=5) and (D=6) Schwarzschild black holes thermodynamics can be modeled by the (d)-dimensional Bose gas, (d=1,2,3,dots,), with the one-particle energy (varepsilon(k)=k^alpha) under the respective conditions (alpha=-d/3) and (alpha=-d/4). In these cases, the free energy of the Bose gas has divergences, and we introduce a cut-off and perform the minimal renormalizations. We also perform renormalizations using analytic regularization and prove that the minimal cut-off renormalization gives the same answer as the analytic regularization by the Riemann zeta-function.
{"title":"Bose gas modeling of the Schwarzschild black hole thermodynamics","authors":"I. Ya. Aref’eva, I. V. Volovich","doi":"10.1134/s0040577924020028","DOIUrl":"https://doi.org/10.1134/s0040577924020028","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Black holes violate the third law of thermodynamics, and this gives rise to difficulties with the microscopic description of their entropy. Recently, it has been shown that the microscopic description of the Schwarzschild black hole thermodynamics in <span>(D = 4)</span> space–time dimensions is provided by the analytic continuation of the entropy of Bose gas with a nonrelativistic one-particle energy to <span>(d =-4)</span> negative spatial dimensions. In this paper, we show that the <span>(D=5)</span> and <span>(D=6)</span> Schwarzschild black holes thermodynamics can be modeled by the <span>(d)</span>-dimensional Bose gas, <span>(d=1,2,3,dots,)</span>, with the one-particle energy <span>(varepsilon(k)=k^alpha)</span> under the respective conditions <span>(alpha=-d/3)</span> and <span>(alpha=-d/4)</span>. In these cases, the free energy of the Bose gas has divergences, and we introduce a cut-off and perform the minimal renormalizations. We also perform renormalizations using analytic regularization and prove that the minimal cut-off renormalization gives the same answer as the analytic regularization by the Riemann zeta-function. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987950","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020077
S. V. Kozyrev
Abstract
A model of population genetics of the Lotka–Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace–Beltrami operator with a Fisher–Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the model of machine learning theory, the model of generative adversarial network (GAN), to the case of populations of generative adversarial networks. The introduced model describes the control of overfitting for generating adversarial networks.
{"title":"Lotka–Volterra model with mutations and generative adversarial networks","authors":"S. V. Kozyrev","doi":"10.1134/s0040577924020077","DOIUrl":"https://doi.org/10.1134/s0040577924020077","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A model of population genetics of the Lotka–Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace–Beltrami operator with a Fisher–Rao metric, that is, the model combines population genetics and information geometry. This model describes a generalization of the model of machine learning theory, the model of generative adversarial network (GAN), to the case of populations of generative adversarial networks. The introduced model describes the control of overfitting for generating adversarial networks. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139988010","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}
Pub Date : 2024-02-27DOI: 10.1134/s0040577924020119
N. M. Khatamov, N. N. Malikov
Abstract
We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules.
摘要 我们将 DNA 分子视为 Potts 模型在 Cayley 树路径上的配置。针对这一模型，我们研究了新的平移不变吉布斯量。我们找到了参数的精确值，从而确定了平移不变吉布斯量的唯一性。每个这样的度量都描述了一组 DNA 分子的状态（相位）。这些吉布斯度量可用于研究 DNA 分子中霍利迪连接的概率分布。
{"title":"Holliday junctions in the set of DNA molecules for new translation-invariant Gibbs measures of the Potts model","authors":"N. M. Khatamov, N. N. Malikov","doi":"10.1134/s0040577924020119","DOIUrl":"https://doi.org/10.1134/s0040577924020119","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a DNA molecule as a configuration of the Potts model on paths of the Cayley tree. For this model, we study new translation-invariant Gibbs measures. We find exact values of the parameter establishing the uniqueness of translation-invariant Gibbs measures. Each such measure describes the state (phase) of a set of DNA molecules. These Gibbs measures are used to study probability distributions of the Holliday junctions in the DNA molecules. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139987949","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}
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