mars-epr 0.0.3b2

A library for computation CW and time resolved spectra

MarS

A toolkit for researchers to simulate, analyze, and explore EPR systems efficiently.

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🚀 Overview

MarS is a Python library for constructing spin systems (electrons and nuclei), defining their magnetic interactions, and simulating Electron Paramagnetic Resonance (EPR) spectra. It supports a wide range of interaction models, efficient batched computations on CPU and GPU, flexible numerical precision (float32 / float64), and tools for both stationary and time-resolved EPR experiments.

🔑 Core Capabilities

Interaction Support

MarS allows users to construct spin systems with the most widely used magnetic interactions:

• Zeeman interaction
• Exchange interaction
• Dipolar interaction
• Zero-field splitting (ZFS)
• Hyperfine interaction

Both isotropic and anisotropic parameters are supported.

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Orientation Support

• Arbitrary orientation of interaction tensors using Euler angles

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Broadening Support

MarS provides several mechanisms to model experimental linewidths:

• Gaussian and Lorentzian line broadening
• Hamiltonian broadening
• Broadening due to distributions of Hamiltonian parameters (so-called strains)

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EPR Spectroscopy Simulation

• Simulation of continuous-wave (CW) EPR spectra
• Support for powder and single-crystal samples
• Field-domain and frequency-domain simulations

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Radiation Polarization Support

• Simulation of spectra under polarized microwave radiation
• Polarization-dependent transition probabilities

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Numerical Precision Control

• Support for float64 and float32 precision

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CPU / CUDA Support

• Support execution on CPU and CUDA-enabled GPUs

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Optimization Framework

• Parameter fitting using Optuna and Nevergrad libraries

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Post-Fitting Analysis

• Tools for analyzing alternative solutions
• Exploration of parameter correlations and degeneracies

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⏱️ Time-Resolved Capabilities

MarS is a comprehensive framework for modeling time-resolved EPR experiments with two complementary computational paradigms.

Relaxation Paradigms

• Population relaxation (Kinetic approach): Evolution of diagonal density matrix elements (population vectors)
• Density matrix relaxation: Full evolution of all density matrix elements. It includes two methods of computations:
  • Rotating frame approximation method
  • Direct propagator calculation method

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Flexible Relaxation Factrors Definition

MarS provides powerful tools for defining complex relaxation processes:

• Population losses (e.g., phosphorescence from triplet states)
• Spontaneous transitions (free transitions satisfying detailed balance)
• Induced transitions (driven transitions not satisfying detailed balance)
• Dephasing (for density matrix formalism)

All mechanisms can be specified in any of several predefined bases or custom transformation matrices.

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Basis Transformation Framework

Comprehensive support for relaxation parameter specification in multiple bases:

• Eigenbasis (eigen): Hamiltonian eigenstates in magnetic field
• Zero-field splitting basis (zfs): Eigenstates of the ZFS operator
• Multiplet basis (multiplet): Total spin and projection states |S, M⟩
• Product basis (product): Individual spin projections |ms1, ms2, ..., msk, is1, ..., ism⟩
• Triplet xyz basis (xyz): Tx, Ty, Tz basis used for triplet molecules
• Zeeman (zeeman): Basis in high magnetic field
• Custom bases: User-defined transformation matrices

Automatic transformation of kinetic matrices and relaxation superoperators between bases.

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Relaxation Algebra

• Summation: Combine multiple relaxation mechanisms defined in different bases
• Multiplication: Construct relaxation mechanism of interacting spin centers
• Concatenation: Construct relaxation mechanism of isolated sub-systems.

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Liouville Space Formalism

• Full support for Liouvillian relaxation superoperators
• Implementation via Lindblad equation for general Markovian evolution
• Automatic enforcement of detailed balance for spontaneous transitions

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Numerical Solvers

Multiple solution strategies optimized for different scenarios:

Population kinetics:

• Stationary solution via matrix exponentiation (for time-independent systems)
• Quasi-stationary iterative solution (for time-dependent rates)
• Adaptive ODE integration (via torchdiffeq, for general time dependence)

Density matrix evolution:

• Rotating frame approximation (computationally efficient, limited to isotropic or close to isotropic g-factors)
• Propagator computation approach (fully general, supports arbitrary anisotropy and relaxation)

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▶️ Getting Started

Installation

git clone https://github.com/ArkadySamsonenkoWork/MarS.git
cd mars
pip install -e <folder

or just

pip install mars-epr

Code Example

import torch
import matplotlib.pyplot as plt
from mars import spin_model, spectra_manager

# Select device and precision
device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
dtype = torch.float64

# Define a simple electron spin system
g_tensor = spin_model.Interaction((2.02, 2.04, 2.06), dtype=dtype, device=device)

system = spin_model.SpinSystem(
    electrons=[0.5],
    g_tensors=[g_tensor],
    dtype=dtype,
    device=device
)

# Create a powder sample
sample = spin_model.MultiOrientedSample(
    base_spin_system=system,
    gauss=0.001,
    lorentz=0.001,
    dtype=dtype,
    device=device
)

# Create spectrum calculator
spectra = spectra_manager.StationarySpectra(
    freq=9.8e9,
    sample=sample,
    dtype=dtype,
    device=device
)

# Magnetic field range
fields = torch.linspace(0.3, 0.4, 1000, device=device, dtype=dtype)

# Compute spectrum
intensity = spectra(sample, fields)

# Plot result
plt.plot(fields.cpu(), intensity.cpu())
plt.xlabel("Magnetic field (T)")
plt.ylabel("Intensity (a.u.)")
plt.title("Simulated CW EPR Spectrum")
plt.show()