Together large-canonical

In Physical statistics, the large-canonical unit are a statistical unit, in which each system is in balance with an external reservoir of energy of particles. That means that the system can exchange energy and Particule S with the tank, in other words, energy and the number of particles is then brought to fluctuate of a system to another of the unit.

This unit is used when the number of particles cannot be fixed, more particularly for the systems made up of Boson S and Fermion S

Introduction

In this unit, one considers that the system is composed of identical Particules, and one introduces the chemical Potentiel, to take into account the variation of the number of particles. The tank must be considered large in front of the system, so that the energy exchange and of particles do not influence the temperature of the tank, and thus on the temperature of the system. The tank must then behave like a Thermostat and impose its temperature on the system.

One regards the Hamiltonien system defined as:

$\backslash \; hat\; H\; =\; \backslash \; sum\_\; \{i=1\}\; ^\; \{NR\}\; \backslash \; hat\; H\; (I)$

where $\backslash \; hat\; H\; (I)\; |I\; \backslash \; rangle\; =\; E\_i\; |I\; \backslash \; rangle$ is the equation of Schrödinger for each particle i.

For each together miscrocopic $|N\; \backslash \; rangle$, one then has the energy and the number of particles associated:

$E\; \backslash \; left\; (|N\; \backslash \; rangle\; \backslash \; right)\; =\; \backslash \; sum\_i\; E\_i\; n\_i$

$NR\; \backslash \; left\; (|N\; \backslash \; rangle\; \backslash \; right)\; =\; \backslash \; sum\_i\; n\_i$

According to whether the system considered is composed of Boson S, or Fermion S, $n\_i$ is subjected to the following conditions:

Observable miscrocopic

Function of partition

The Fonction of partition is defined as being:

$\backslash \; Xi\; =\; \backslash \; sum\_\; \{\backslash$

Probability of a microphone-state

The probability so that the system is in a microphone-state I is defined by:

$p\_i\; =\; \backslash \; frac\; \{e^\; \{-\; \backslash \; beta\; \backslash \; left\; (E\_i\; -\; \backslash \; driven\; \backslash \; right)\; n\_i\}\}\; \{\backslash \; Xi\}$

where $\backslash \; sum\_\; \{I\}\; p\_i\; \backslash \; =\; \backslash \; 1$

Observable macroscopic

See too

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