Spectra of nonlocally bound quantum systems
Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Sowa, A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2011 |
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| Schlagwörter: |
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| Anmerkung: |
© Pleiades Publishing, Ltd. 2011 |
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| Übergeordnetes Werk: |
Enthalten in: Russian journal of mathematical physics - SP MAIK Nauka/Interperiodica, 1993, 18(2011), 2 vom: Juni, Seite 227-241 |
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| Übergeordnetes Werk: |
volume:18 ; year:2011 ; number:2 ; month:06 ; pages:227-241 |
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| DOI / URN: |
10.1134/S1061920811020117 |
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| 520 | |a Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. | ||
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10.1134/S1061920811020117 doi (DE-627)OLC2049271107 (DE-He213)S1061920811020117-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sowa, A. verfasserin aut Spectra of nonlocally bound quantum systems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2011 Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. Quantum System Zeta Function Composite System Dirichlet Series Composite State Enthalten in Russian journal of mathematical physics SP MAIK Nauka/Interperiodica, 1993 18(2011), 2 vom: Juni, Seite 227-241 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:18 year:2011 number:2 month:06 pages:227-241 https://doi.org/10.1134/S1061920811020117 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_70 AR 18 2011 2 06 227-241 |
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10.1134/S1061920811020117 doi (DE-627)OLC2049271107 (DE-He213)S1061920811020117-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sowa, A. verfasserin aut Spectra of nonlocally bound quantum systems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2011 Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. Quantum System Zeta Function Composite System Dirichlet Series Composite State Enthalten in Russian journal of mathematical physics SP MAIK Nauka/Interperiodica, 1993 18(2011), 2 vom: Juni, Seite 227-241 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:18 year:2011 number:2 month:06 pages:227-241 https://doi.org/10.1134/S1061920811020117 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_70 AR 18 2011 2 06 227-241 |
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10.1134/S1061920811020117 doi (DE-627)OLC2049271107 (DE-He213)S1061920811020117-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sowa, A. verfasserin aut Spectra of nonlocally bound quantum systems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2011 Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. Quantum System Zeta Function Composite System Dirichlet Series Composite State Enthalten in Russian journal of mathematical physics SP MAIK Nauka/Interperiodica, 1993 18(2011), 2 vom: Juni, Seite 227-241 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:18 year:2011 number:2 month:06 pages:227-241 https://doi.org/10.1134/S1061920811020117 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_70 AR 18 2011 2 06 227-241 |
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10.1134/S1061920811020117 doi (DE-627)OLC2049271107 (DE-He213)S1061920811020117-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sowa, A. verfasserin aut Spectra of nonlocally bound quantum systems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2011 Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. Quantum System Zeta Function Composite System Dirichlet Series Composite State Enthalten in Russian journal of mathematical physics SP MAIK Nauka/Interperiodica, 1993 18(2011), 2 vom: Juni, Seite 227-241 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:18 year:2011 number:2 month:06 pages:227-241 https://doi.org/10.1134/S1061920811020117 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_70 AR 18 2011 2 06 227-241 |
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10.1134/S1061920811020117 doi (DE-627)OLC2049271107 (DE-He213)S1061920811020117-p DE-627 ger DE-627 rakwb eng 530 510 VZ Sowa, A. verfasserin aut Spectra of nonlocally bound quantum systems 2011 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Pleiades Publishing, Ltd. 2011 Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. Quantum System Zeta Function Composite System Dirichlet Series Composite State Enthalten in Russian journal of mathematical physics SP MAIK Nauka/Interperiodica, 1993 18(2011), 2 vom: Juni, Seite 227-241 (DE-627)190282460 (DE-600)1291704-7 (DE-576)285631713 1061-9208 nnns volume:18 year:2011 number:2 month:06 pages:227-241 https://doi.org/10.1134/S1061920811020117 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-MAT GBV_ILN_70 AR 18 2011 2 06 227-241 |
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Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. © Pleiades Publishing, Ltd. 2011 |
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Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. © Pleiades Publishing, Ltd. 2011 |
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Abstract We discuss a class of nonlinear and nonlocal models for the dynamics of a composite quantum system. The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. In particular, as an interesting offshoot, this structure furnishes a nontautological immersion of fundamental number-theoretic functions into the quantum formalism. © Pleiades Publishing, Ltd. 2011 |
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Spectra of nonlocally bound quantum systems |
| url |
https://doi.org/10.1134/S1061920811020117 |
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false |
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190282460 |
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| doi_str |
10.1134/S1061920811020117 |
| up_date |
2024-07-03T22:07:22.598Z |
| _version_ |
1803597321442689024 |
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The models in question depend on the following constituents: on two subsystem Hamiltonians (denoted by H and Ĥ), an analytic function (f), and a real parameter (s). As demonstrated elsewhere before, the stationary states can be described in these models fairly explicitly. In this article, we build upon that result, and discuss the topological as well as statistical characteristics of the spectra. Here, we concentrate on the special case f = log. It turns out that an energy spectrum of the nonlocally bound system substantially differs from that of its components. Indeed, we show rigorously that, if H is the harmonic oscillator and Ĥ is completely degenerate with one energy level, then the energy spectrum of the composite system has the topology of the Cantor set (for s > 2). In addition, we show that, if H is replaced by the logarithm of the harmonic oscillator, then the spectrum consists of finitely many intervals separated by gaps (for s sufficiently large). In the last case, the key analytic object is the series Σn−s. 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