• Corpus ID: 251442712

# Density Matrix of the Fermionic Harmonic Oscillator

@inproceedings{Saleh2022DensityMO,
title={Density Matrix of the Fermionic Harmonic Oscillator},
author={Batool A. Abu Saleh},
year={2022}
}
The path integral technique is used to derive a possible expression for the density operator of the fermionic harmonic oscillator. In terms of the Grassmann variables, the fermionic density operator can be written as: 𝜌 𝐹 (𝛽) = 𝑐 ∗ (𝛽)𝑐(𝛽) ± 𝑐 ∗ (𝛽)𝑐(𝛽) 𝑒 −𝛽𝜔 , where +(−) means that the sum over all antiperiodic (periodic) orbits. Our density operator is then used to obtain the usual fermionic partition function which describes the fermionic oscillator in thermal equilibrium. Also…

## References

SHOWING 1-10 OF 18 REFERENCES

### The Method of Second Quantization

In the usual formalism of quantum mechanics, the first quantization formalism, observables are represented by operators and the wave functions are normal functions. In the method of second

### Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

• M. Putz
• Physics
International journal of molecular sciences
• 2009
The practical specializations for quantum free and harmonic motions, along with the smearing justification for the Bohr’s quantum stability postulate, advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the many-electronic systems.

### Space-Time Approach to Non-Relativistic Quantum Mechanics

Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which

### Duality, partial supersymmetry, and arithmetic number theory

We find examples of duality among quantum theories that are related to arithmetic functions by identifying distinct Hamiltonians that have identical partition functions at suitably related coupling

### Geometry and Quantum Field Theory (PDF)

Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of

### Path Integrals and Their Application to Dissipative Quantum Systems

The coupling of a system to its environment is a recurrent subject in this collection of lecture notes. The consequences of such a coupling are threefold. First of all, energy may irreversibly be

### An asymptotic expansion for the first derivative of the generalized Riemann Zeta function

An asymptotic expansion for the partial derivative a( q)/13z of the generalized Riemann zeta function t( q), for all negative integer values of Z, is obtained. The generalized Riemann zeta function

Building upon an analytical technique introduced by Chung and Peschel [Phys. Rev. B 64, 064412 (2001)], we calculated the many-body density matrix ${\ensuremath{\rho}}_{B}$ of a finite block of B