Fractal behaviour of quantum paths in statistical physics
The path integral formalism is used to describe the statistical properties of an ideal gas of spinless particles. It is shown that the quantum paths exhibit the same properties in non-relativistic and relativistic domains provided the creation of new particles is avoided. Some quantities associat...
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| Дата: | 2000 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2000
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121007 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Fractal behaviour of quantum paths in statistical physics / J.P. Badiali // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 545-558. — Бібліогр.: 19 назв. — англ. |
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irk-123456789-1210072017-06-14T03:04:04Z Fractal behaviour of quantum paths in statistical physics Badiali, J.P. The path integral formalism is used to describe the statistical properties of an ideal gas of spinless particles. It is shown that the quantum paths exhibit the same properties in non-relativistic and relativistic domains provided the creation of new particles is avoided. Some quantities associated with the paths are introduced, they have a simple meaning if the quantity βh , where β is the reverse of the temperature, is considered as an ordinary time. The relation between the velocity on the path and the momentum is not the usual one, an extra term appears showing that the thermostat can not fix the average value of this velocity although all the thermodynamic quantities have their traditional values. The paths describe fluctuating trajectories on which the particles do not follow the equation of motion. For time intervals much shorter than βh we recover the properties of the Brownian motion. The trajectories are located in space in a volume restricted by the Compton wavelength for the short distances and the thermal de Broglie wavelength for the largest ones. It is shown that the time-energy uncertainty is verified on the quantum paths. This suggests that the density matrix obtained by quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual route. Strong arguments are given showing that βh can be considered as an ordinary time and not as a formal quantity having the same dimension as time. This paper shows that for a time scale of 10 femtoseconds a totally new physics can be expected at room temperature. In addition it is suggested that the ratio h/kB may play a decisive role in the foundation of a covariant statistical physics. Використовується формалiзм iнтегралiв по шляхах для опису iдеального газу безспiнових частинок. Показано, що квантовi шляхи мають однаковi властивостi у релятивiстичнiй та нерелятивiстичнiй областях, за умови, що немає утворення нових частинок. Введено деякi величини, пов’язанi зi шляхами. Цi величини мають просте значення, якщо величина βh , де β – обернена температура, розглядається як звичайний час. Спiввiдношення мiж швидкiстю на шляху та iмпульсом не є звичним, появляється додатковий член, який показує, що термостат не може фiксувати середнє значення цiєї швидкостi. Хоча усi термодинамiчнi величини приймають традицiйнi значення. Шляхи описують флуктуацiйнi траєкторiї, на яких частинки пiдкоряються рiвнянням руху. Для iнтервалiв часу, значно коротших за βh , ми вiдтворюємо властивостi Броунiвського руху. Траєкторiї є обмеженi у просторi мiж об’ємом порядку комптонiвської довжини хвилi для коротких вiдстаней та об’ємом порядку температурної довжини хвилi де Бройля для найбiльших вiдстаней. Показано, що невизначенiсть мiж часом та енергiєю справджується на квантових шляхах. Це вказує на те, що матриця густини, отримана квантуванням класичної канонiчної функцiї розподiлу, не має бути цiлком еквiвалентною до матрицi густини, отриманої звиклим способом. Наведено переконливi аргументи на користь того, що βh може розглядатись як звичайний час, а не як формальна величина, що має розмiрнiсть часу. Ця стаття показує, що для iнтервалiв часу порядку 10 фемтосекунд, можна очiкувати цiлком нову фiзику при кiмнатнiй температурi. Також цi результати наводять на думку, що вiдношення ~/kb може вiдiгравати вирiшальну роль у побудовi коварiантної статистичної фiзики. 2000 Article Fractal behaviour of quantum paths in statistical physics / J.P. Badiali // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 545-558. — Бібліогр.: 19 назв. — англ. 1607-324X DOI:10.5488/CMP.3.3.545 PACS: 03.65.Ca, 05.30.-d, 05.70.-a, 47.53.+n http://dspace.nbuv.gov.ua/handle/123456789/121007 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The path integral formalism is used to describe the statistical properties of
an ideal gas of spinless particles. It is shown that the quantum paths exhibit
the same properties in non-relativistic and relativistic domains provided the
creation of new particles is avoided. Some quantities associated with the
paths are introduced, they have a simple meaning if the quantity βh , where
β is the reverse of the temperature, is considered as an ordinary time. The
relation between the velocity on the path and the momentum is not the
usual one, an extra term appears showing that the thermostat can not fix
the average value of this velocity although all the thermodynamic quantities
have their traditional values. The paths describe fluctuating trajectories on
which the particles do not follow the equation of motion. For time intervals
much shorter than βh we recover the properties of the Brownian motion.
The trajectories are located in space in a volume restricted by the Compton
wavelength for the short distances and the thermal de Broglie wavelength
for the largest ones. It is shown that the time-energy uncertainty is verified
on the quantum paths. This suggests that the density matrix obtained by
quantification of the classical canonical distribution function via the path integral formalism should not be totally identical to that obtained via the usual
route. Strong arguments are given showing that βh can be considered as
an ordinary time and not as a formal quantity having the same dimension
as time. This paper shows that for a time scale of 10 femtoseconds a totally new physics can be expected at room temperature. In addition it is
suggested that the ratio h/kB may play a decisive role in the foundation of
a covariant statistical physics. |
| format |
Article |
| author |
Badiali, J.P. |
| spellingShingle |
Badiali, J.P. Fractal behaviour of quantum paths in statistical physics Condensed Matter Physics |
| author_facet |
Badiali, J.P. |
| author_sort |
Badiali, J.P. |
| title |
Fractal behaviour of quantum paths in statistical physics |
| title_short |
Fractal behaviour of quantum paths in statistical physics |
| title_full |
Fractal behaviour of quantum paths in statistical physics |
| title_fullStr |
Fractal behaviour of quantum paths in statistical physics |
| title_full_unstemmed |
Fractal behaviour of quantum paths in statistical physics |
| title_sort |
fractal behaviour of quantum paths in statistical physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2000 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/121007 |
| citation_txt |
Fractal behaviour of quantum paths in statistical physics / J.P. Badiali // Condensed Matter Physics. — 2000. — Т. 3, № 3(23). — С. 545-558. — Бібліогр.: 19 назв. — англ. |
| series |
Condensed Matter Physics |
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2023-10-18T20:38:42Z |
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