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Canonical quantization of nonlinear many-body systems
1Istituto Nazionale di Fisica della Materia (INFM) and Dipartimento di Fisica Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Turin, Italy. antonio.scarfone@polito.it
Summary
This study quantifies interacting particles using a novel kinetic interaction principle (KIP). It introduces nonlinear Schrödinger equations (NSEs) and demonstrates their gauge equivalence to real-nonlinearity NSEs for specific conditions.
Area of Science:
- Quantum mechanics
- Statistical physics
- Nonlinear dynamics
Background:
- The kinetic interaction principle (KIP) offers a new framework for describing particle systems.
- Classical systems require a quantum mechanical description for accurate modeling.
Purpose of the Study:
- To quantize a classical system of interacting particles governed by the KIP.
- To introduce and analyze a class of nonlinear Schrödinger equations (NSEs) derived from the KIP.
- To explore the mathematical properties and equivalences of these NSEs.
Main Methods:
- Canonical quantization applied to a classical system.
- Derivation of nonlinear Schrödinger equations (NSEs) with complex nonlinearities.
- Analysis of Ehrenfest relations and constants of motion.
- Application of a nonlinear gauge transformation.
Main Results:
- A class of complex-nonlinearity NSEs is introduced, describing KIP-governed particle systems.
- Ehrenfest relations and constants of motion are derived for the model.
- Gauge equivalence is established between complex and real-nonlinearity NSEs under specific conditions (constant diffusion, linear drift).
Conclusions:
- The KIP provides a foundation for a quantum description of interacting particles.
- The introduced NSEs offer a framework for studying these systems.
- Gauge transformations simplify the mathematical description of these nonlinear systems.