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Extremum-entropy-based Heisenberg-like uncertainty relations
- Publication Year :
- 2015
- Publisher :
- arXiv, 2015.
-
Abstract
- In this work we use the extremization method of various information-theoretic measures (Fisher information, Shannon entropy, Tsallis entropy) for $d$-dimensional quantum systems, which complementary describe the spreading of the quantum states of natural systems. Under some given constraints, usually one or two radial expectation values, this variational method allows us to determine an extremum-entropy distribution, which is the \textit{least-biased} one to characterize the state among all those compatible with the known data. Then we use it, together with the spin-dependent uncertainty-like relations of Daubechies-Thakkar type, as a tool to obtain relationships between the position and momentum radial expectation values of the type $\langle r^{\alpha}\rangle^{\frac{k}{\alpha}}\langle p^k\rangle\geq f(k,\alpha,q,N), q=2s+1$, for $d$-dimensional systems of $N$ fermions with spin $s$. The resulting uncertainty-like products, which take into account both spatial and spin degrees of freedom of the fermionic constituents of the system, are shown to often improve the best corresponding relationships existing in the literature.<br />Comment: Accepted for publication in Journal of Physics A
- Subjects :
- Statistics and Probability
Quantum Physics
Tsallis entropy
Degrees of freedom (statistics)
General Physics and Astronomy
FOS: Physical sciences
Statistical and Nonlinear Physics
01 natural sciences
010305 fluids & plasmas
symbols.namesake
Variational method
Quantum state
Position (vector)
Modeling and Simulation
0103 physical sciences
symbols
Statistical physics
010306 general physics
Fisher information
Quantum Physics (quant-ph)
Quantum
Mathematical Physics
Mathematics
Spin-½
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....452007463acce8424ecb866cf5d58c31
- Full Text :
- https://doi.org/10.48550/arxiv.1511.03866