We investigate the low temperature behavior of a heavy particle in a fermionic bath. Two competing effects dominate the physics: a shakeup of the Fermi sea (orthogonality catastrophe) destroys the coherence, while the recoil of the particle tends to restore it by reducing the available phase space for scattering events. An effective action is considered which exactly implements these two aspects. In one dimension the coherence of the particle is destroyed---the propagator decays algebraically for long times. In two and higher dimensions coherent propagation survives.We investigate the low temperature behavior of a heavy particle in a fermionic bath. Two competing effects dominate the physics: a shakeup of the Fermi sea (orthogonality catastrophe) destroys the coherence, while the recoil of the particle tends to restore it by reducing the available phase space for scattering events. An effective action is considered which exactly implements these two aspects. In one dimension the coherence of the particle is destroyed---the propagator decays algebraically for long times. In two and higher dimensions coherent propagation survives.

arXiv:cond-mat/9502034Physical Review LettersSep 4, 199532 citations

Quantum Principle of Least Action in Dynamic Theories With Higher Derivatives

Natalia N. Gorobey, Alexander S. Lukyanenko, Goltsev, A. V.

A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator.A generalized canonical form of action of dynamic theories with higher derivatives is proposed, which does not require the introduction of additional dynamic variables. This form is the initial point for the construction of quantum theory, in which the state of motion of the system is described by the wave functional on its trajectories in the configuration space, and the functional itself is an eigenvector of the action operator. The Pais-Uhlenbeck oscillator is considered as the simplest model. For this case, the correspondence between the new form of quantum theory and "ordinary" quantum mechanics has been established in the local limit, when the Pais-Uhlenbeck oscillator is reduced to the "ordinary" harmonic oscillator.

arXiv:2404.09608Apr 15, 20240 citations

Quantum binding in low dimensions

A. R. P. Rau

American Journal of PhysicsOct 1, 19901 citation

Quantum Walks in Low Dimension

Tatsuya Tate

Trends in mathematicsJan 1, 20160 citations

SPEEDUP Code for Calculation of Transition Amplitudes via the Effective Action Approach

Antun Balaž, Ivana Vasić, Danica Stojiljković +3 more

We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order $p$ =18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schrödinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.We present Path Integral Monte Carlo C code for calculation of quantum mechanical transition amplitudes for 1D models. The SPEEDUP C code is based on the use of higher-order short-time effective actions and implemented to the maximal order $p$=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schrödinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.

arXiv:1105.0542Communications in Computational PhysicsMay 22, 20126 citations

p

=18 in the time of propagation (Monte Carlo time step), which substantially improves the convergence of discretized amplitudes to their exact continuum values. Symbolic derivation of higher-order effective actions is implemented in SPEEDUP Mathematica codes, using the recursive Schrödinger equation approach. In addition to the general 1D quantum theory, developed Mathematica codes are capable of calculating effective actions for specific models, for general 2D and 3D potentials, as well as for a general many-body theory in arbitrary number of spatial dimensions.