# Semiclassical formula for quantum tunneling in asymmetric double-well potentials

@article{Rastelli2012SemiclassicalFF, title={Semiclassical formula for quantum tunneling in asymmetric double-well potentials}, author={Gianluca Rastelli}, journal={Physical Review A}, year={2012}, volume={86} }

Despite quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric double-well potentials. In the regime of strong localization, we derive an succinct analytical formula based on the WKB semi-classical approach. Two different examples of asymmetric potentials are discussed: when the two localized levels are degenerate or not. For the first case, we also discuss a time-dependent… Expand

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#### References

SHOWING 1-10 OF 60 REFERENCES

Tunneling in Complex Systems

- Physics
- 1998

Some general aspects of quantum tunnelling and coherence - application to the BEC atomic gases, A.J. Leggett tunnelling in two-dimensions, S.C. Creagh quantum environments - spin baths, oscillator… Expand

Macroscopic tunnel splittings in superconducting phase qubits.

- Physics, Medicine
- Physical review letters
- 2005

It is shown that macroscopic resonant tunneling in the extremely asymmetric double-well potential of the phase qubit can have observational consequences that are strikingly similar to the observed data. Expand

Macroscopic Quantum Tunneling

- Physics
- 2002

Macroscopic quantum phenomena are particularly important when considering the problem of Schrödinger’s cat. This book contains a coherent and self-contained account of such phenomena, focusing on the… Expand

Quantum Tunneling in Complex Systems: The Semiclassical Approach

- Physics
- 2007

Semiclassical Approximation.- Tunneling in the Energy Domain.- Wave-packet Tunneling in Real-time.- Tunneling in Open Systems: Thermodynamical Approaches.- Tunneling in Open Systems: Dynamics.-… Expand

Tunnel splittings for one-dimensional potential wells revisited

- Physics, Mathematics
- 2000

The Wentzel–Kramers–Brillouin and instanton answers for the tunnel splitting of the ground state in a symmetric double-well potential are both reduced to an expression involving only functionals of… Expand

Quantum Theory of Tunneling

- Physics
- 2003

A Brief History of Quantum Tunneling Some Basic Questions Concerning Quantum Tunneling Simple Solvable Problems Time-Dependence of the Wave Function in One-Dimensional Tunneling Semiclassical… Expand

Quantum mechanical barrier problems

- Physics
- 1987

Three different types of quantum mechanical barrier systems are considered as eigenvalue problems. First, the real energy levels of the local ground states in a weakly biased double-well potential… Expand

Direct observation of tunneling and nonlinear self-trapping in a single bosonic Josephson junction.

- Physics, Medicine
- Physical review letters
- 2005

A novel nonlinear effect known as macroscopic quantum self-trapping, which leads to the inhibition of large amplitude tunneling oscillations in superconducting and superfluid Josephson junctions is confirmed. Expand

Coupled quantum dots as quantum gates

- Physics
- 1999

We consider a quantum-gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We… Expand

Some properties of double-Morse potentials

- Physics
- 1998

In the framework of various exact and approximate methods, the properties of the quasi-exactly solvable double-Morse potential are discussed. The relation between the hidden algebraic structure of… Expand