Pub Date : 2024-11-12DOI: 10.1016/j.aop.2024.169841
C.D. Fosco, G. Hansen
We study pair creation out of the vacuum, for a system consisting of a massive Dirac field in dimensions, contained between a pair of perfectly reflecting boundaries, one of them oscillating. After analyzing some general properties of the vacuum-decay process, we evaluate the corresponding transition amplitude in a Magnus expansion of the -matrix. We show how this yields, besides the single-pair creation amplitude, multipair ones, as well as corrections to the single pair amplitude.
We also apply it to obtain an approximate, yet explicitly unitary expression for the Bogoliubov transformation between the in and out Fock spaces.
我们研究了一个由 1+1 维的大质量狄拉克场组成的系统，该系统包含在一对完美反射边界之间，其中一个边界在振荡。在分析了真空衰变过程的一些一般性质之后，我们评估了 S 矩阵的马格努斯展开中相应的过渡振幅。我们还利用它得到了进出福克空间之间博格柳波夫变换的近似但明确的单位表达式。
{"title":"Fermionic dynamical Casimir effect: Magnus expansion","authors":"C.D. Fosco, G. Hansen","doi":"10.1016/j.aop.2024.169841","DOIUrl":"10.1016/j.aop.2024.169841","url":null,"abstract":"<div><div>We study pair creation out of the vacuum, for a system consisting of a massive Dirac field in <span><math><mrow><mn>1</mn><mo>+</mo><mn>1</mn></mrow></math></span> dimensions, contained between a pair of perfectly reflecting boundaries, one of them oscillating. After analyzing some general properties of the vacuum-decay process, we evaluate the corresponding transition amplitude in a Magnus expansion of the <span><math><mi>S</mi></math></span>-matrix. We show how this yields, besides the single-pair creation amplitude, multipair ones, as well as corrections to the single pair amplitude.</div><div>We also apply it to obtain an approximate, yet explicitly unitary expression for the Bogoliubov transformation between the <em>in</em> and <em>out</em> Fock spaces.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169841"},"PeriodicalIF":3.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-12DOI: 10.1016/j.aop.2024.169848
Zixuan Ding , Donghao Wang , Liangliang Lu , Mengyao Li , Yongchun Tao , Fengliang Huang
We theoretically study the Josephson effect of massive pseudospin-1 fermions in a superconductor/ferromagnet/superconductor (S/F/S) junction based on the dice lattice, including - and -type mass terms with the magnitude . For the -type fermions, it is found that, in the absence of ferromagnetic exchange field , the supercurrent is effectively inhibited by or the junction length . In the presence of , state transition can be realized by modulating , , or . The -induced state transition occurs more frequently for a larger or . Particularly, the inhibition of supercurrent caused by still remains for a large . In the doping case, corresponding to a nonzero , the -induced state transition may disappear for a large or . With increased, the inhibition caused by diminishes for a small whereas intensifies for a large . In addition, the supercurrent features for the -type fermions distinct from those for the -type fermions are demonstrated.
我们从理论上研究了基于骰子晶格的超导体/铁磁体/超导体（S/F/S）结中大质量伪ospin-1费米子的约瑟夫森效应，其中包括量级为m的Sz型和+U型质量项。研究发现，对于Sz型费米子，在没有铁磁交换场h的情况下，超电流会受到m或结长度L的有效抑制。在掺杂的情况下，对应于非零 EF，m 诱导的状态转变可能会在较大的 h 或 L 下消失。随着 EF 的增加，m 导致的抑制作用在较小的 h 下减弱，而在较大的 h 下增强。
{"title":"Josephson effect of massive pseudospin-1 fermions in the ferromagnetic dice lattice","authors":"Zixuan Ding , Donghao Wang , Liangliang Lu , Mengyao Li , Yongchun Tao , Fengliang Huang","doi":"10.1016/j.aop.2024.169848","DOIUrl":"10.1016/j.aop.2024.169848","url":null,"abstract":"<div><div>We theoretically study the Josephson effect of massive pseudospin-1 fermions in a superconductor/ferromagnet/superconductor (S/F/S) junction based on the dice lattice, including <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>- and <span><math><mrow><mo>+</mo><mi>U</mi></mrow></math></span>-type mass terms with the magnitude <span><math><mi>m</mi></math></span>. For the <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>-type fermions, it is found that, in the absence of ferromagnetic exchange field <span><math><mi>h</mi></math></span>, the supercurrent is effectively inhibited by <span><math><mi>m</mi></math></span> or the junction length <span><math><mi>L</mi></math></span>. In the presence of <span><math><mi>h</mi></math></span>, <span><math><mrow><mn>0</mn><mo>−</mo><mi>π</mi></mrow></math></span> state transition can be realized by modulating <span><math><mi>h</mi></math></span>, <span><math><mi>m</mi></math></span>, or <span><math><mi>L</mi></math></span>. The <span><math><mi>m</mi></math></span>-induced state transition occurs more frequently for a larger <span><math><mi>h</mi></math></span> or <span><math><mi>L</mi></math></span>. Particularly, the inhibition of supercurrent caused by <span><math><mi>m</mi></math></span> still remains for a large <span><math><mi>m</mi></math></span>. In the doping case, corresponding to a nonzero <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span>, the <span><math><mi>m</mi></math></span>-induced state transition may disappear for a large <span><math><mi>h</mi></math></span> or <span><math><mi>L</mi></math></span>. With <span><math><msub><mrow><mi>E</mi></mrow><mrow><mi>F</mi></mrow></msub></math></span> increased, the inhibition caused by <span><math><mi>m</mi></math></span> diminishes for a small <span><math><mi>h</mi></math></span> whereas intensifies for a large <span><math><mi>h</mi></math></span>. In addition, the supercurrent features for the <span><math><mrow><mo>+</mo><mi>U</mi></mrow></math></span>-type fermions distinct from those for the <span><math><msub><mrow><mi>S</mi></mrow><mrow><mi>z</mi></mrow></msub></math></span>-type fermions are demonstrated.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169848"},"PeriodicalIF":3.0,"publicationDate":"2024-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-08DOI: 10.1016/j.aop.2024.169837
Shuai Li , Rui Tian , Min Liu , Maksims Arzamasovs , Liangchao Chen , Bo Liu
A five-level M-type scheme in atomic ensembles is proposed to generate a one-dimensional bipartite superradiance lattice in momentum space. By taking advantage of this tunable atomic system, we show that various types of Su-Schrieffer-Heeger (SSH) model, including the standard SSH and extended SSH model, can be realized. Interestingly, it is shown that through changing the Rabi frequencies and detunings in our proposed scheme, there is a topological phase transition from topological trivial regime with winding number being 0 to topological non-trivial regime with winding number being 2. Furthermore, a robust flat band with higher winding number (being 2) can be achieved in the above topological non-trivial regime, where the superradiance spectra can be utilized as a tool for experimental detection. Our proposal would provide a promising approach to explore new physics, such as fractional topological phases, in the flat bands with higher topological number.
{"title":"Topological flat band with higher winding number in a superradiance lattice","authors":"Shuai Li , Rui Tian , Min Liu , Maksims Arzamasovs , Liangchao Chen , Bo Liu","doi":"10.1016/j.aop.2024.169837","DOIUrl":"10.1016/j.aop.2024.169837","url":null,"abstract":"<div><div>A five-level M-type scheme in atomic ensembles is proposed to generate a one-dimensional bipartite superradiance lattice in momentum space. By taking advantage of this tunable atomic system, we show that various types of Su-Schrieffer-Heeger (SSH) model, including the standard SSH and extended SSH model, can be realized. Interestingly, it is shown that through changing the Rabi frequencies and detunings in our proposed scheme, there is a topological phase transition from topological trivial regime with winding number being 0 to topological non-trivial regime with winding number being 2. Furthermore, a robust flat band with higher winding number (being 2) can be achieved in the above topological non-trivial regime, where the superradiance spectra can be utilized as a tool for experimental detection. Our proposal would provide a promising approach to explore new physics, such as fractional topological phases, in the flat bands with higher topological number.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169837"},"PeriodicalIF":3.0,"publicationDate":"2024-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651359","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-07DOI: 10.1016/j.aop.2024.169838
Abolfath Hosseinzadeh , S.A. Jafari
We use Boltzmann theory to study the semi-classical dynamics of electrons in a two-dimensional (2D) tilted Dirac material in which the tilt varies in space. The spatial variation of the tilt parameter induces a non-trivial spacetime geometry on the background of which the electrons roam about. As the first manifestation of gravito-electric phenomena, we find a geometric planar Hall effect according to which a current flows in a direction transverse to the chemical potential gradient and is proportional to component of the emergent spacetime structure. The longitudinal conductivity contains information about the gravitational red-shift factors. Furthermore, in the absence of externally applied electric field there can be “free-fall” or zero-bias currents that can be used as detectors of terahertz radiation.
{"title":"Semiclassical transport in two-dimensional Dirac materials with spatially variable tilt","authors":"Abolfath Hosseinzadeh , S.A. Jafari","doi":"10.1016/j.aop.2024.169838","DOIUrl":"10.1016/j.aop.2024.169838","url":null,"abstract":"<div><div>We use Boltzmann theory to study the semi-classical dynamics of electrons in a two-dimensional (2D) tilted Dirac material in which the tilt varies in space. The spatial variation of the tilt parameter induces a non-trivial spacetime geometry on the background of which the electrons roam about. As the first manifestation of gravito-electric phenomena, we find a geometric planar Hall effect according to which a current flows in a direction transverse to the chemical potential gradient and is proportional to <span><math><msup><mrow><mi>g</mi></mrow><mrow><mi>x</mi><mi>y</mi></mrow></msup></math></span> component of the emergent spacetime structure. The longitudinal conductivity contains information about the gravitational red-shift factors. Furthermore, in the absence of externally applied electric field there can be “free-fall” or zero-bias currents that can be used as detectors of terahertz radiation.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169838"},"PeriodicalIF":3.0,"publicationDate":"2024-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-11-05DOI: 10.1016/j.aop.2024.169836
S. Viaggiu
In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature , proportional to the Bekenstein-Hawking one, is such that . As a consequence, according to other similar proposals in the literature, only a kind of Bose–Einstein condensate (BEC) can exactly support the black hole entropy.
{"title":"The fate for the interior content of a Black Hole from one-quarter entropy area-law","authors":"S. Viaggiu","doi":"10.1016/j.aop.2024.169836","DOIUrl":"10.1016/j.aop.2024.169836","url":null,"abstract":"<div><div>In this paper we continue investigations concerning the physical nature of the black hole entropy. In particular, in order to depict massless excitations (gravitons) leading to the one-quarter entropy area law, we use a mechanical statistical approach. As a first result, we obtain that, starting with a radiation field, we cannot exactly obtain the one-quarter factor in entropy area law. In the aforementioned framework, the correct black hole entropy is obtained only in the case where the internal temperature <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub></math></span>, proportional to the Bekenstein-Hawking one, is such that <span><math><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>→</mo><mn>0</mn></mrow></math></span>. As a consequence, according to other similar proposals in the literature, only a kind of Bose–Einstein condensate (BEC) can exactly support the black hole entropy.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169836"},"PeriodicalIF":3.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-05DOI: 10.1016/j.aop.2024.169834
S. Habib Mazharimousavi
This research revisits the thin-shell wormhole connecting two Minkowski spacetimes — originally introduced by Matt Visser. Upon setting a particular timelike hypersurface with a de-sitter-induced line element, the corresponding thin-shell wormhole (TSW) possesses a minimum radius and a uniform surface energy–momentum tensor in the form of dark energy. The bounded from below radius for the throat implies that it does not collapse. The profile curve of the hypersurface is a Catenary in plane where and are the radial coordinate and the proper time on the throat, respectively. It is also shown that while the throat is dynamic, the surface energy–momentum tensor of the dark energy is in the form of an effective cosmological constant in the spherically symmetric TSW. The -dimensional cylindrically symmetric TSW with a similar throat profile shares the same features as its spherical counterpart, however, its uniform surface energy–momentum tensor does not mimic an effective cosmological constant. The higher-dimensional generalization of the spherically symmetric TSW admits the same properties as in the -dimensional one.
{"title":"Thin-shell wormholes with non-collapsing dark energy throats connecting flat Minkowski spacetimes","authors":"S. Habib Mazharimousavi","doi":"10.1016/j.aop.2024.169834","DOIUrl":"10.1016/j.aop.2024.169834","url":null,"abstract":"<div><div>This research revisits the thin-shell wormhole connecting two Minkowski spacetimes — originally introduced by Matt Visser. Upon setting a particular timelike hypersurface with a de-sitter-induced line element, the corresponding thin-shell wormhole (TSW) possesses a minimum radius and a uniform surface energy–momentum tensor in the form of dark energy. <em>The bounded from below radius for the throat implies that it does not collapse.</em> The <span><math><mrow><mi>r</mi><mo>−</mo><mi>τ</mi></mrow></math></span> profile curve of the hypersurface is a Catenary in <span><math><mrow><mi>r</mi><mo>−</mo><mi>τ</mi></mrow></math></span> plane where <span><math><mi>r</mi></math></span> and <span><math><mi>τ</mi></math></span> are the radial coordinate and the proper time on the throat, respectively. It is also shown that while the throat is dynamic, the surface energy–momentum tensor of the dark energy is in the form of an effective cosmological constant in the spherically symmetric TSW. The <span><math><mn>4</mn></math></span>-dimensional cylindrically symmetric TSW with a similar throat profile shares the same features as its spherical counterpart, however, its uniform surface energy–momentum tensor does not mimic an effective cosmological constant. The higher-dimensional generalization of the spherically symmetric TSW admits the same properties as in the <span><math><mn>4</mn></math></span>-dimensional one.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169834"},"PeriodicalIF":3.0,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651362","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-04DOI: 10.1016/j.aop.2024.169828
F. Bagarello , F. Gargano , L. Saluto
In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a -symmetric chemical potential . In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for and for . We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken -symmetry is discussed, in connection with the strength of .
在本文中，我们为存在磁场的石墨烯紧密束缚模型以及包含 PT 对称化学势 V 的变形模型构建了不同类别的相干和双相干态，特别是在 V=0 和 V≠0 的情况下，在构建这些态时考虑了系统缺乏合适基态所带来的问题。我们引入了梯形算子，这些算子在我们的语境中非常有效，而且我们特别表明，这些算子的选择可以产生哈密顿的因式分解。我们结合 V 的强度讨论了断裂和未断裂 PT 对称性的作用。
{"title":"Coherent states of graphene layer with and without a PT-symmetric chemical potential","authors":"F. Bagarello , F. Gargano , L. Saluto","doi":"10.1016/j.aop.2024.169828","DOIUrl":"10.1016/j.aop.2024.169828","url":null,"abstract":"<div><div>In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a <span><math><mrow><mi>P</mi><mi>T</mi></mrow></math></span>-symmetric chemical potential <span><math><mi>V</mi></math></span>. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for <span><math><mrow><mi>V</mi><mo>=</mo><mn>0</mn></mrow></math></span> and for <span><math><mrow><mi>V</mi><mo>≠</mo><mn>0</mn></mrow></math></span>. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken <span><math><mrow><mi>P</mi><mi>T</mi></mrow></math></span>-symmetry is discussed, in connection with the strength of <span><math><mi>V</mi></math></span>.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169828"},"PeriodicalIF":3.0,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142651363","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-01DOI: 10.1016/j.aop.2024.169832
Babak Parvin
A two-level atom is enclosed in a single-mode optical cavity, and the occurring processes in this system have been theoretically examined in the steady-state. In the non-resonance case and in several different instances, the lasing and non-lasing regimes are specified in the semiclassical approximation in the parameter space. The behavior of the system is fully described for the time when there are a small or large number of photons in the cavity. The semiclassical approximation is shown in two different frameworks, and its results are well confirmed by the quantum simulations when there are many photons in the cavity. To observe the change in the behavior of the emitted light near the laser threshold, the second order coherence function and the Fano factor have been used. In explaining the antibunching process, the explicit form of the second order coherence function has been obtained in two different representations. This function is equal in both representations to the lowest order and its findings are in good agreement with the quantum model.
{"title":"Linear and quadratic behaviors in a two-level laser","authors":"Babak Parvin","doi":"10.1016/j.aop.2024.169832","DOIUrl":"10.1016/j.aop.2024.169832","url":null,"abstract":"<div><div>A two-level atom is enclosed in a single-mode optical cavity, and the occurring processes in this system have been theoretically examined in the steady-state. In the non-resonance case and in several different instances, the lasing and non-lasing regimes are specified in the semiclassical approximation in the parameter space. The behavior of the system is fully described for the time when there are a small or large number of photons in the cavity. The semiclassical approximation is shown in two different frameworks, and its results are well confirmed by the quantum simulations when there are many photons in the cavity. To observe the change in the behavior of the emitted light near the laser threshold, the second order coherence function and the Fano factor have been used. In explaining the antibunching process, the explicit form of the second order coherence function has been obtained in two different representations. This function is equal in both representations to the lowest order and its findings are in good agreement with the quantum model.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"471 ","pages":"Article 169832"},"PeriodicalIF":3.0,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-01DOI: 10.1016/j.aop.2024.169830
H.C. Rosu, J. de la Cruz
The singular parametric oscillators obtained from the one-parameter Darboux deformation/ transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using and as seed solutions. The corresponding Ermakov–Lewis integrability problem of these parametric oscillators is also studied. It is shown that their Ermakov–Lewis invariants do not depend on the deformation parameter and are singularity-free.
{"title":"Singular parametric oscillators from the one-parameter Darboux transformation of the classical harmonic oscillator","authors":"H.C. Rosu, J. de la Cruz","doi":"10.1016/j.aop.2024.169830","DOIUrl":"10.1016/j.aop.2024.169830","url":null,"abstract":"<div><div>The singular parametric oscillators obtained from the one-parameter Darboux deformation/ transformation effected upon the classical harmonic oscillator are introduced and discussed in some detail using <span><math><mrow><mo>sin</mo><mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mo>cos</mo><mrow><mo>(</mo><msub><mrow><mi>ω</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>t</mi><mo>)</mo></mrow></mrow></math></span> as seed solutions. The corresponding Ermakov–Lewis integrability problem of these parametric oscillators is also studied. It is shown that their Ermakov–Lewis invariants do not depend on the deformation parameter and are singularity-free.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"470 ","pages":"Article 169830"},"PeriodicalIF":3.0,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553860","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 : 2024-11-01DOI: 10.1016/j.aop.2024.169831
Xin Gu , Yuan-Yuan Liu , Hong-Wei Ke , Wen-Du Li , Wu-Sheng Dai
This paper proposes a method for constructing exactly solvable time-dependent oscillator families based on the invariant operator method and the duality method. An exactly solvable time-dependent oscillator family contains an infinite number of exactly solvable time-dependent oscillators. As a byproduct, we also construct exactly solvable Ermakov–Pinney equation families.
{"title":"Exactly solvable time-dependent oscillator family","authors":"Xin Gu , Yuan-Yuan Liu , Hong-Wei Ke , Wen-Du Li , Wu-Sheng Dai","doi":"10.1016/j.aop.2024.169831","DOIUrl":"10.1016/j.aop.2024.169831","url":null,"abstract":"<div><div>This paper proposes a method for constructing exactly solvable time-dependent oscillator families based on the invariant operator method and the duality method. An exactly solvable time-dependent oscillator family contains an infinite number of exactly solvable time-dependent oscillators. As a byproduct, we also construct exactly solvable Ermakov–Pinney equation families.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"470 ","pages":"Article 169831"},"PeriodicalIF":3.0,"publicationDate":"2024-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142553861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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