Development of Quantum Field Theory Methods
for Statistical Physics
Our research group pioneers the application of quantum field theory (QFT) methods
to address profoundly nonlinear problems in statistical physics. These methods are
indispensable for systems exhibiting infinitely many degrees of freedom — a hallmark
shared with quantum field theory itself.
Key Challenges & Applications
We focus on problems where strong nonlinearity dominates, such as:
- Fully Developed Turbulence: The Navier-Stokes equations reveal solution instabilities at high velocities, leading to the formation of interacting eddies (vortices). These eddies fundamentally alter the fluid's mean flow properties. Our goal is the statistical characterization of these eddies . determining their probability distributions and scaling laws.
- Critical Phenomena: Including phase transitions and universal scaling near critical points.
- Wave Propagation in Critical Media: Understanding how waves behave in systems near criticality.
- Goldstone Mode Singularities: Arising from spontaneous symmetry breaking.
- Nonlinear Plasma Phenomena: Complex collective behavior in charged particle systems.
In all these systems, strong fluctuations and infinite correlation lengths emerge, rendering conventional perturbative approaches insufficient.
Our Methodological Toolkit
To tackle these challenges, we leverage a powerful arsenal of advanced QFT techniques:
- Nonlinear Schwinger-Dyson Equations
- Functional Legendre Transforms
- Non-Perturbative Renormalization Group (RG) Methods
- Instanton and Semiclassical Analysis
- Resurgent Asymptotics and Resummation Techniques
- Advanced Diagrammatic Expansions
By adapting and extending these sophisticated tools from quantum field theory, we develop novel theoretical frameworks to unravel the complex statistical behavior of strongly correlated classical and quantum systems.
People who work in this field:
D. Sc. professor Loran Adzhemyan
D. Sc. professor Mikhail Nalimov
Ph. D. docent Marina Komarova
|
