fermions

This program calculates statistical properties of fermions in equilibrium. It's designed to compute macroscopic parameters such as number density (n), energy density (ρ), and pressure (p) as functions of temperature (T) and chemical potential (μ) for a given fermion mass (m) and spin (s). The calculations are performed for different temperature regimes (lowT, normal, highT), allowing for the exploration of different analytical approximation methods.

Installation and Usage

Requirements

Essential Software:

• Fortran Compiler: A Fortran compiler supporting Fortran 2008 or later (e.g., gfortran, ifort, pgfortran). Preferable compiler is gfortran
• CMake: The CMake build system is required for building the project.

Additional Requirements (for plotting and optional performance):

To generate plots of the results using the provided plot.py script and to optionally improve performance, you will need the following:

• Python 3.x: The Python 3 programming language.
• NumPy: The fundamental package for scientific computing in Python.
• Matplotlib: A comprehensive library for creating static, interactive, and animated visualizations in Python.
• LAPACK (Recommended): The Linear Algebra PACKage (LAPACK) library is highly recommended for optimal performance. While not strictly mandatory, its inclusion significantly enhances the speed of certain calculations.

Installation Instructions (Linux):

The commands to install the required software packages will vary depending on your Linux distribution. Note: You will likely need sudo rights (administrator privileges) to install system-level packages. Here are examples for some common distributions:

Essential Packages:

Debian/Ubuntu (apt):

sudo apt update
sudo apt install gfortran cmake

Fedora/CentOS/RHEL (dnf/yum):

sudo dnf update  #(use 'sudo yum update' for older RHEL/CentOS versions)
sudo dnf install gfortran cmake

Arch Linux (pacman):

sudo pacman -Syu
sudo pacman -S gfortran cmake

Additional Packages (Python and LAPACK):

After installing the essential packages above, install the remaining requirements:

pip3 install numpy matplotlib
sudo apt install liblapack-dev  # Debian/Ubuntu; use appropriate command for your distribution (see below)

Installing LAPACK (Distribution-Specific):

• Debian/Ubuntu: sudo apt install liblapack-dev
• Fedora/CentOS/RHEL: sudo dnf install lapack-devel (or sudo yum install lapack-devel for older versions)
• Arch Linux: sudo pacman -S lapack

Step 1: Clone the Repository

git clone https://github.com/StepanRepo/fermions.git
cd fermions

Step 2: Build the Project

1. Ensure you have CMake and a Fortran compiler installed.
2. Create a build directory and compile the project:

cd build
cmake ..
make

3. The compiled executable fermions will be placed in the root directory of the repository.

Step 3: Configure the Program

The fermions program uses default.cfg for customization. This file allows users to set physical and numerical parameters for calculations. The file follows the Fortran namelist format and must begin with &config_nml and end with /.

Configuration Parameters:

General Format:

&config_nml
parameter_name = value
/

Parameters:

• output_dir: Directory for output files.

  • Example: output_dir = "results"

• regime: Temperature regime.

  • Options: "lowT", "normal", "highT".
  • Example: regime = "highT"

• Tmin and Tmax: Temperature range (in Kelvin).

  • Example: Tmin = 0.5, Tmax = 100.0

• discr: Number of points in the temperature range.

  • Example: discr = 200

• mu: Chemical potential (in energy units).

  • Example: mu = 1e-10

• m: Particle mass (in grams).

  • Example: m = 1.6726219e-24 (proton mass).

• s: Particle spin.

  • Example: s = 1.5

• nu: De Broglie frequency (in Hz). Only used when m = 0.

  • Example: nu = 1e16

Example Configuration

&config_nml
output_dir = "results"
regime = "highT"
Tmin = 0.5
Tmax = 100.0
discr = 200
mu = 1e-10
m = 1.6726219e-24
s = 0.5
nu = 1e16
/

Notes

• Comments: Add comments with !. Example: Tmin = 0.1 ! Minimum temperature.
• Output Directory: Ensure the directory exists or create it manually.
• Massless Particles: Set m = 0 and define nu.
• Discretization: Higher discr increases resolution but may slow computation.

How to Use the Results

The fermions program generates output files containing calculated physical properties of fermions based on the configuration provided in default.cfg. These results can be used for analysis, visualization, and further study.

Output Files

File Format

• The program produces .dat files in the directory specified by the output_dir parameter in default.cfg.

• Each .dat file contains tabulated data with the following columns:

  1. Temperature (T): The temperature values (in Kelvin).
  2. Chemical Potential (μ): The chemical potential values (in energy units).
  3. Number Density (n): The number density of fermions (in cm⁻³).
  4. Mass Density (ρ): The mass density of fermions (in g·cm⁻³).
  5. Pressure (p): The pressure of fermions (in dyn·cm⁻²).

• Example:

  T          μ              n              ρ            p
  0.1        1.00e-15       1.23e+23       1.98e-12     1.45e+10
  0.2        1.00e-15       2.34e+23       3.21e-12     2.76e+10

Plotting the Results

• Use the provided Python script (plot.py) to generate plots for quick visualization.
• The script processes all .dat files in the output directory and produces .pdf files with the following plots:
  1. Number Density (n) vs Temperature (T).
  2. Energy Density (ρ) vs Temperature (T).
  3. Pressure (p) vs Temperature (T).

Running the Python Script

python3 plot.py

• The .pdf files will be saved in the same directory as the .dat files.
• Example output file: results/data.pdf (if output_dir is set to results).

The generated plots will include:

• X-axis: Temperature (T, in Kelvin).
• Y-axis: The respective physical property (n, ρ, or p).