Pub Date : 2019-09-01DOI: 10.1142/S1230161219500136
K. Modi
These are my recollections of working with George Sudarshan from 2002 to 2008 when I was a PhD student in his group. During these years I learnt a lot of physics and also was a witness to some remarkable occurrences.
{"title":"George Sudarshan and Quantum Dynamics","authors":"K. Modi","doi":"10.1142/S1230161219500136","DOIUrl":"https://doi.org/10.1142/S1230161219500136","url":null,"abstract":"These are my recollections of working with George Sudarshan from 2002 to 2008 when I was a PhD student in his group. During these years I learnt a lot of physics and also was a witness to some remarkable occurrences.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"82 1","pages":"1950013:1-1950013:19"},"PeriodicalIF":0.8,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78328087","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 : 2019-09-01DOI: 10.1142/S123016121950015X
F. Fagnola, C. Mora
We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form, and we prove the uniqueness of the solution to the nonautonomous linear adjoint quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form. Moreover, we obtain rigorously the Maxwell–Bloch equations from the mean field laser equation.
{"title":"Basic Properties of a Mean Field Laser Equation","authors":"F. Fagnola, C. Mora","doi":"10.1142/S123016121950015X","DOIUrl":"https://doi.org/10.1142/S123016121950015X","url":null,"abstract":"We study the nonlinear quantum master equation describing a laser under the mean field approximation. The quantum system is formed by a single mode optical cavity and two level atoms, which interact with reservoirs. Namely, we establish the existence and uniqueness of the regular solution to the nonlinear operator equation under consideration, as well as we get a probabilistic representation for this solution in terms of a mean field stochastic Schrödinger equation. To this end, we find a regular solution for the nonautonomous linear quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form, and we prove the uniqueness of the solution to the nonautonomous linear adjoint quantum master equation in Gorini–Kossakowski–Sudarshan–Lindblad form. Moreover, we obtain rigorously the Maxwell–Bloch equations from the mean field laser equation.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"26 1","pages":"1950015:1-1950015:30"},"PeriodicalIF":0.8,"publicationDate":"2019-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83059724","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 : 2019-07-24DOI: 10.1142/S1230161219500057
J. Mackowiak
A mean-field theory is developed for a Bose liquid enclosed in a large vessel 𝒱. In accord with liquid structure concepts of Mitus et al., the liquid in 𝒱 is assumed to consist of adjacent macroscopic subregions Λk. In each subregion the bosons perform a locally ordered motion with prevailing orientation k + x, which varies randomly when passing from one subregion to another. |k| is constant, whereas temperature dependence of |x| is governed by a mean-field theory (MFT). The theory is applied to simulate HeI heat capacity CV (T) at T > Tλ = 2.17 K and CV (T) singularity at [Formula: see text]. The MFT numerical heat capacity Cn(T) = ΔE/ΔT exhibits behaviour characteristic of a singularity at [Formula: see text]: rapid increase with decreasing ΔT. Apart from [Formula: see text], good agreement of Cn(T) with CV(T) experimental plot is also found above Tλ, at T ∊ (Tλ, 3K].
{"title":"Bose Liquid Mean-Field Theory with Application to HeI","authors":"J. Mackowiak","doi":"10.1142/S1230161219500057","DOIUrl":"https://doi.org/10.1142/S1230161219500057","url":null,"abstract":"A mean-field theory is developed for a Bose liquid enclosed in a large vessel 𝒱. In accord with liquid structure concepts of Mitus et al., the liquid in 𝒱 is assumed to consist of adjacent macroscopic subregions Λk. In each subregion the bosons perform a locally ordered motion with prevailing orientation k + x, which varies randomly when passing from one subregion to another. |k| is constant, whereas temperature dependence of |x| is governed by a mean-field theory (MFT). The theory is applied to simulate HeI heat capacity CV (T) at T > Tλ = 2.17 K and CV (T) singularity at [Formula: see text]. The MFT numerical heat capacity Cn(T) = ΔE/ΔT exhibits behaviour characteristic of a singularity at [Formula: see text]: rapid increase with decreasing ΔT. Apart from [Formula: see text], good agreement of Cn(T) with CV(T) experimental plot is also found above Tλ, at T ∊ (Tλ, 3K].","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"153 1","pages":"1950005:1-1950005:20"},"PeriodicalIF":0.8,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78602900","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 : 2019-07-24DOI: 10.1142/S1230161219500070
A. Wichert
We present a case study of quantum-like probabilities that are motivated by quantum cognition. We introduce quantum-like evolution that is l2 norm preserving but in which the matrix does not need to be unitary. We show how to map any 2 × 2 stochastic matrix to an l2 norm preserving balanced phase matrix that maps real vectors of length one into complex vectors of length one. Quantum-like evolution can simulate a probability distribution of open system in which the operator is not unitary but norm preserving. Such a kind of behaviour is studied in quantum cognition. By tensor product higher dimensional balanced phase matrices can be built. Quantum-like evolution can simulate either unitary open one by coding the phase of input vector into the phase of a balanced phase matrix, a Markov chain or an alternative evolution that can lead to fixed, periodic or chaotic behaviour resulting in strange oscillations.
{"title":"Principles of Quantum-like Evolution","authors":"A. Wichert","doi":"10.1142/S1230161219500070","DOIUrl":"https://doi.org/10.1142/S1230161219500070","url":null,"abstract":"We present a case study of quantum-like probabilities that are motivated by quantum cognition. We introduce quantum-like evolution that is l2 norm preserving but in which the matrix does not need to be unitary. We show how to map any 2 × 2 stochastic matrix to an l2 norm preserving balanced phase matrix that maps real vectors of length one into complex vectors of length one. Quantum-like evolution can simulate a probability distribution of open system in which the operator is not unitary but norm preserving. Such a kind of behaviour is studied in quantum cognition. By tensor product higher dimensional balanced phase matrices can be built. Quantum-like evolution can simulate either unitary open one by coding the phase of input vector into the phase of a balanced phase matrix, a Markov chain or an alternative evolution that can lead to fixed, periodic or chaotic behaviour resulting in strange oscillations.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"94 1","pages":"1950007:1-1950007:21"},"PeriodicalIF":0.8,"publicationDate":"2019-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75923417","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 : 2019-07-21DOI: 10.1142/S1230161219500173
F. Cosmo, Alberto Ibort, G. Marmo
Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.
{"title":"Groupoids and Coherent States","authors":"F. Cosmo, Alberto Ibort, G. Marmo","doi":"10.1142/S1230161219500173","DOIUrl":"https://doi.org/10.1142/S1230161219500173","url":null,"abstract":"Schwinger’s algebra of selective measurements has a natural interpretation in terms of groupoids. This approach is pushed forward in this paper to show that the theory of coherent states has a natural setting in the framework of groupoids. Thus given a quantum mechanical system with associated Hilbert space determined by a representation of a groupoid, it is shown that any invariant subset of the group of invertible elements in the groupoid algebra determines a family of generalized coherent states provided that a completeness condition is satisfied. The standard coherent states for the harmonic oscillator as well as generalized coherent states for f-oscillators are exemplified in this picture.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"72 1","pages":"1950017:1-1950017:22"},"PeriodicalIF":0.8,"publicationDate":"2019-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83285862","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 : 2019-07-12DOI: 10.1142/S1230161219500112
G. Marmo, S. Pascazio
George Sudarshan was an eclectic thinker, and one of the most profound physicists of the last century. We review here a small part of his oeuvre, focusing on his pioneering contributions to the quantum Zeno effect, quantum channels (the Kraus–Sudarshan representation) and quantum semigroups (the Gorini–Kossakowski–Lindblad–Sudarshan equation). These topics are of crucial importance in the booming field of quantum mechanics and applications.
{"title":"The Legacy of George Sudarshan","authors":"G. Marmo, S. Pascazio","doi":"10.1142/S1230161219500112","DOIUrl":"https://doi.org/10.1142/S1230161219500112","url":null,"abstract":"George Sudarshan was an eclectic thinker, and one of the most profound physicists of the last century. We review here a small part of his oeuvre, focusing on his pioneering contributions to the quantum Zeno effect, quantum channels (the Kraus–Sudarshan representation) and quantum semigroups (the Gorini–Kossakowski–Lindblad–Sudarshan equation). These topics are of crucial importance in the booming field of quantum mechanics and applications.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"17 1","pages":"1950011:1-1950011:10"},"PeriodicalIF":0.8,"publicationDate":"2019-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82660784","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 : 2019-06-01DOI: 10.1142/S1230161219500094
Kyouhei Ohmura, Noboru Watanabe
The classical dynamical mutual entropy measures the average of information content going through a channel. Classical Markovian sources are important in communication theory since they constitute reasonable models for languages. In this paper, we define the quantum dynamical mutual entropy through quantum Markov chains, and we calculate it for several simple models.
{"title":"Quantum Dynamical Mutual Entropy Based on AOW Entropy","authors":"Kyouhei Ohmura, Noboru Watanabe","doi":"10.1142/S1230161219500094","DOIUrl":"https://doi.org/10.1142/S1230161219500094","url":null,"abstract":"The classical dynamical mutual entropy measures the average of information content going through a channel. Classical Markovian sources are important in communication theory since they constitute reasonable models for languages. In this paper, we define the quantum dynamical mutual entropy through quantum Markov chains, and we calculate it for several simple models.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"14 1","pages":"1950009:1-1950009:16"},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73098205","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 : 2019-06-01DOI: 10.1142/S1230161219500100
T. Kamizawa
The analysis of an open quantum system can be by far difficult if the dimension of the system Hilbert space is large or infinite. However, in some cases the dynamics on a finite-dimensional Hilbert space can be decomposed into a block-diagonal form, which simplifies the system structure. In this presentation, we will study several criteria for the complete reducibility and, in addition, a computational method for a basis of each simplified component to apply for the analysis of open quantum systems. An important point of these tools is that they are “effective” methods (one can complete the task in a finite number of steps).
{"title":"Reducibility Criteria and a Construction Method for the Analysis of Open Quantum Systems","authors":"T. Kamizawa","doi":"10.1142/S1230161219500100","DOIUrl":"https://doi.org/10.1142/S1230161219500100","url":null,"abstract":"The analysis of an open quantum system can be by far difficult if the dimension of the system Hilbert space is large or infinite. However, in some cases the dynamics on a finite-dimensional Hilbert space can be decomposed into a block-diagonal form, which simplifies the system structure. In this presentation, we will study several criteria for the complete reducibility and, in addition, a computational method for a basis of each simplified component to apply for the analysis of open quantum systems. An important point of these tools is that they are “effective” methods (one can complete the task in a finite number of steps).","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"19 1","pages":"1950010:1-1950010:15"},"PeriodicalIF":0.8,"publicationDate":"2019-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78798545","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 : 2019-05-14DOI: 10.1142/S1230161219500124
M. Asorey, P. Facchi, G. Marmo
The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.
{"title":"Topological Order, Mixed States and Open Systems","authors":"M. Asorey, P. Facchi, G. Marmo","doi":"10.1142/S1230161219500124","DOIUrl":"https://doi.org/10.1142/S1230161219500124","url":null,"abstract":"The role of mixed states in topological quantum matter is less known than that of pure quantum states. Generalisations of topological phases appearing in pure states have received attention in the literature only quite recently. In particular, it is still unclear whether the generalisation of the Aharonov–Anandan phase for mixed states due to Uhlmann plays any physical role in the behaviour of the quantum systems. We analyse, from a general viewpoint, topological phases of mixed states and the robustness of their invariance. In particular, we analyse the role of these phases in the behaviour of systems with periodic symmetry and their evolution under the influence of an environment preserving its crystalline symmetries.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"2 1","pages":"1950012:1-1950012:15"},"PeriodicalIF":0.8,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81966758","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 : 2019-05-09DOI: 10.1142/S1230161219500185
V. Pathak, Anil Shaji
Convex combinations of completely positive (CP) as well as CP-divisible, continuous time dynamical maps arising from collision models are investigated. While the individual maps are both CP and Markovian we find that convex combinations remain CP but not necessarily Markovian. Examples of such combinations for qubit dynamical maps arising from collisional models are worked out and the invertibility, CP-divisibility, P-divisibility as well as Markovian properties of such maps are explored.
{"title":"Non-Markovian Open Dynamics from Collision Models","authors":"V. Pathak, Anil Shaji","doi":"10.1142/S1230161219500185","DOIUrl":"https://doi.org/10.1142/S1230161219500185","url":null,"abstract":"Convex combinations of completely positive (CP) as well as CP-divisible, continuous time dynamical maps arising from collision models are investigated. While the individual maps are both CP and Markovian we find that convex combinations remain CP but not necessarily Markovian. Examples of such combinations for qubit dynamical maps arising from collisional models are worked out and the invertibility, CP-divisibility, P-divisibility as well as Markovian properties of such maps are explored.","PeriodicalId":54681,"journal":{"name":"Open Systems & Information Dynamics","volume":"39 1","pages":"1950018:1-1950018:19"},"PeriodicalIF":0.8,"publicationDate":"2019-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73878765","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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