Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1228.81027
Bender, Carl M.; Brody, Dorje C.; Jones, Hugh F.; Meister, Bernhard K.
Faster than Hermitian quantum mechanics. (English)
[J] Phys. Rev. Lett. 98, No. 4, Article ID 040403, 4 p. (2007). ISSN 0031-9007; ISSN 1079-7114/e

Summary: Given an initial quantum state $|\psi_I\rangle$ and a final quantum state $|\psi_F\rangle$, there exist Hamiltonians $H$ under which $|\psi_I\rangle$ evolves into $|\psi_F\rangle$. Consider the following quantum brachistochrone problem: subject to the constraint that the difference between the largest and smallest eigenvalues of $H$ is held fixed, which $H$ achieves this transformation in the least time $\tau$? For Hermitian Hamiltonians $\tau$ has a nonzero lower bound. However, among non-Hermitian $\cal P\cal T$-symmetric Hamiltonians satisfying the same energy constraint, $\tau$ can be made arbitrarily small without violating the time-energy uncertainty principle. This is because for such Hamiltonians the path from $|\psi_I\rangle$ to $|\psi_F\rangle$ can be made short. The mechanism described here is similar to that in general relativity in which the distance between two space-time points can be made small if the points are connected by a wormhole. This result may have applications in quantum computing.

MSC 2000:: *81P05 General and philosophical topics in quantum theory
81P68 Quantum computation and quantum cryptography

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]