Particle in a Box with Dissipation

Gustavo V. López, M. Murguía, Modesto Antonio Sosa

Using Schrödinger's quantization method, the Hamiltonian of a particle moving in a one-dimensional dissipative medium is quantized in a box of length L and at first order on dissipation strength. Expressions for , and |ψ|2 are obtained in terms of the dissipation parameter. A treatment for the case of free particle motion with friction is presented.

David O Hayward

J. Sabio, L. Borda, F. Guinea +1 more

We analyze the phase diagram of a quantum particle confined to a finite chain and subjected to a dissipative environment described by an ohmic spectral function. Analytical and numerical techniques are employed to explore both the perturbative and nonperturbative regimes of the model. For small dissipation of the coupling to the environment leads to a narrowing of the density distribution and to a displacement toward the center of the array of accessible sites. For large values of the dissipation, we find a phase transition to a doubly degenerate phase, which reflects the formation of an inhomogeneous effective potential within the array.

James M. Feagin

Gert‐Ludwig Ingold

Introduction Path Integrals - Introduction - Propagator - Free Particle - Path Integral Representation of Quantum Mechanics - Particle on a Ring - Particle in a Box - Driven Harmonic Oscillator - Semiclassical Approximation - Imaginary Time Path Integral Dissipative Systems - Introduction - Environment as Collection of Harmonic Oscillators - Effective Action Damped Harmonic Oscillator - Partition Function - Ground State Energy and Density of States - Position Autocorrelation Function