The deterministic dynamics of a single-particle quantum ensemble is equivalent to the stochastic one due to the indistinguishability of quantum particles
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2021
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911496579055616 |
|---|---|
| author | Chuprikov, N. L. |
| author_facet | Chuprikov, N. L. |
| contents | It is shown that the wave function describing the pure state of a single-particle quantum ensemble, in addition to statistical restrictions, imposes restrictions on the particle momentum at points in the configuration space $\mathbb{R}^3$: at time $t$, each point $\mathbf{r}$ is a ``meeting'' point of two (non-interacting) particles of the ensemble with momenta $\mathbf{p}_1(\mathbf{r},t)$ and $\mathbf{p}_2(\mathbf{r},t)$. Their peculiarity is that the velocities $\mathbf{p}_1(\mathbf{r},t)/m$ and $\mathbf{p}_2(\mathbf{r},t)/m$ coincide with the velocities $\mathbf{b}(\mathbf{r},t)$ and $\mathbf{b}_*(\mathbf{r},t)$, which are introduced in Nelson's stochastic approach as key characteristics of frictionless Brownian particle motion. This means that the instantaneous dynamics of a pair of non-interacting quantum particles of an ensemble at point $\mathbf{r}$ at time $t$, due to their fundamental indistinguishability, is equivalent to the collision of two classical Brownian particles. And since this is true at all times for all points in $\mathbb{R}^3$, the unitary deterministic dynamics of a single-particle quantum ensemble is equivalent to a stochastic process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_06221 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The deterministic dynamics of a single-particle quantum ensemble is equivalent to the stochastic one due to the indistinguishability of quantum particles Chuprikov, N. L. Quantum Physics It is shown that the wave function describing the pure state of a single-particle quantum ensemble, in addition to statistical restrictions, imposes restrictions on the particle momentum at points in the configuration space $\mathbb{R}^3$: at time $t$, each point $\mathbf{r}$ is a ``meeting'' point of two (non-interacting) particles of the ensemble with momenta $\mathbf{p}_1(\mathbf{r},t)$ and $\mathbf{p}_2(\mathbf{r},t)$. Their peculiarity is that the velocities $\mathbf{p}_1(\mathbf{r},t)/m$ and $\mathbf{p}_2(\mathbf{r},t)/m$ coincide with the velocities $\mathbf{b}(\mathbf{r},t)$ and $\mathbf{b}_*(\mathbf{r},t)$, which are introduced in Nelson's stochastic approach as key characteristics of frictionless Brownian particle motion. This means that the instantaneous dynamics of a pair of non-interacting quantum particles of an ensemble at point $\mathbf{r}$ at time $t$, due to their fundamental indistinguishability, is equivalent to the collision of two classical Brownian particles. And since this is true at all times for all points in $\mathbb{R}^3$, the unitary deterministic dynamics of a single-particle quantum ensemble is equivalent to a stochastic process. |
| title | The deterministic dynamics of a single-particle quantum ensemble is equivalent to the stochastic one due to the indistinguishability of quantum particles |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2111.06221 |