Time Asymmetric Quantum Mechanics
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac...
Збережено в:
| Дата: | 2011 |
|---|---|
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
|
| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147386 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147386 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1473862019-02-15T01:24:09Z Time Asymmetric Quantum Mechanics Bohm, A.R. Gadella, M. Kielanowski, P. The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t₀≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics. 2011 Article Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 81Q65 http://dspace.nbuv.gov.ua/handle/123456789/147386 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The meaning of time asymmetry in quantum physics is discussed. On the basis of a mathematical theorem, the Stone-von Neumann theorem, the solutions of the dynamical equations, the Schrödinger equation (1) for states or the Heisenberg equation (6a) for observables are given by a unitary group. Dirac kets require the concept of a RHS (rigged Hilbert space) of Schwartz functions; for this kind of RHS a mathematical theorem also leads to time symmetric group evolution. Scattering theory suggests to distinguish mathematically between states (defined by a preparation apparatus) and observables (defined by a registration apparatus (detector)). If one requires that scattering resonances of width Γ and exponentially decaying states of lifetime τ=h/Γ should be the same physical entities (for which there is sufficient evidence) one is led to a pair of RHS's of Hardy functions and connected with it, to a semigroup time evolution t₀≤t<∞, with the puzzling result that there is a quantum mechanical beginning of time, just like the big bang time for the universe, when it was a quantum system. The decay of quasi-stable particles is used to illustrate this quantum mechanical time asymmetry. From the analysis of these processes, we show that the properties of rigged Hilbert spaces of Hardy functions are suitable for a formulation of time asymmetry in quantum mechanics. |
| format |
Article |
| author |
Bohm, A.R. Gadella, M. Kielanowski, P. |
| spellingShingle |
Bohm, A.R. Gadella, M. Kielanowski, P. Time Asymmetric Quantum Mechanics Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Bohm, A.R. Gadella, M. Kielanowski, P. |
| author_sort |
Bohm, A.R. |
| title |
Time Asymmetric Quantum Mechanics |
| title_short |
Time Asymmetric Quantum Mechanics |
| title_full |
Time Asymmetric Quantum Mechanics |
| title_fullStr |
Time Asymmetric Quantum Mechanics |
| title_full_unstemmed |
Time Asymmetric Quantum Mechanics |
| title_sort |
time asymmetric quantum mechanics |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147386 |
| citation_txt |
Time Asymmetric Quantum Mechanics / A.R. Bohm, M. Gadella, P. Kielanowski // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 28 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT bohmar timeasymmetricquantummechanics AT gadellam timeasymmetricquantummechanics AT kielanowskip timeasymmetricquantummechanics |
| first_indexed |
2023-05-20T17:27:37Z |
| last_indexed |
2023-05-20T17:27:37Z |
| _version_ |
1796153339366342656 |