Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line
The model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other classes of potential. The analytical and...
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MDPI AG
2024-09-01
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| Series: | Condensed Matter |
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| Online Access: | https://www.mdpi.com/2410-3896/9/4/35 |
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| author | Krzysztof Pomorski Łukasz Pluszyński Eryk Hałubek |
| author_facet | Krzysztof Pomorski Łukasz Pluszyński Eryk Hałubek |
| author_sort | Krzysztof Pomorski |
| collection | DOAJ |
| description | The model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other classes of potential. The analytical and numerical validation of Kron’s second model is conducted for different shapes of particle-confining potentials in the one-dimensional case using an LTspice simulator. Thus, there remains potential for obtaining solutions in two- and three-dimensional cases. Here, a circuit model representing a linearized Ginzburg–Landau equation is given. Kron’s second model is generalized by the introduction of linear and non-linear resistive elements. This transforms the deformed Schrödinger equation into a linear dissipative Schrödinger equation and its non-linear form. The quantum mechanical roton problem is the main result of this work and is formulated by means of classical physical states naturally present in the LC classical circular electrical transmission line. The experimental verification of Kron’s model is confirmed. |
| format | Article |
| id | doaj-art-82bc3eada66047dfabf44aab220a6b23 |
| institution | DOAJ |
| issn | 2410-3896 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Condensed Matter |
| spelling | doaj-art-82bc3eada66047dfabf44aab220a6b232025-08-20T02:50:59ZengMDPI AGCondensed Matter2410-38962024-09-01943510.3390/condmat9040035Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission LineKrzysztof Pomorski0Łukasz Pluszyński1Eryk Hałubek2Institute of Physics, Lodz University of Technology, 90-924 Lodz, PolandQuantum Hardware Systems, 94-056 Lodz, PolandInstitute of Physics, Lodz University of Technology, 90-924 Lodz, PolandThe model presented by Gabriel Kron in 1945 is an example of an analog computer simulating quantum phenomena on a hardware level. It uses passive RLC elements to construct a hardware solver for the problem of quantum particles confined by rectangular or other classes of potential. The analytical and numerical validation of Kron’s second model is conducted for different shapes of particle-confining potentials in the one-dimensional case using an LTspice simulator. Thus, there remains potential for obtaining solutions in two- and three-dimensional cases. Here, a circuit model representing a linearized Ginzburg–Landau equation is given. Kron’s second model is generalized by the introduction of linear and non-linear resistive elements. This transforms the deformed Schrödinger equation into a linear dissipative Schrödinger equation and its non-linear form. The quantum mechanical roton problem is the main result of this work and is formulated by means of classical physical states naturally present in the LC classical circular electrical transmission line. The experimental verification of Kron’s model is confirmed.https://www.mdpi.com/2410-3896/9/4/35analog computerdifferential equationquantum mechanics simulationanalog electronicsSchrödinger modelGinzburg–Landau equation |
| spellingShingle | Krzysztof Pomorski Łukasz Pluszyński Eryk Hałubek Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line Condensed Matter analog computer differential equation quantum mechanics simulation analog electronics Schrödinger model Ginzburg–Landau equation |
| title | Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line |
| title_full | Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line |
| title_fullStr | Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line |
| title_full_unstemmed | Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line |
| title_short | Towards the Construction of an Analog Solver for the Schrödinger and Ginzburg–Landau Equations Based on a Transmission Line |
| title_sort | towards the construction of an analog solver for the schrodinger and ginzburg landau equations based on a transmission line |
| topic | analog computer differential equation quantum mechanics simulation analog electronics Schrödinger model Ginzburg–Landau equation |
| url | https://www.mdpi.com/2410-3896/9/4/35 |
| work_keys_str_mv | AT krzysztofpomorski towardstheconstructionofananalogsolverfortheschrodingerandginzburglandauequationsbasedonatransmissionline AT łukaszpluszynski towardstheconstructionofananalogsolverfortheschrodingerandginzburglandauequationsbasedonatransmissionline AT erykhałubek towardstheconstructionofananalogsolverfortheschrodingerandginzburglandauequationsbasedonatransmissionline |