Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Ghatak, Ananya; Mandal, Bhabani Prasad

doi:10.1088/0253-6102/59/5/03

Cited by 12 publications

(7 citation statements)

References 57 publications

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“…In this section we will apply our analysis to the following asymmetric twodimensional Hamilton operator H (and the respective partners H + , iH, (iH) + ) considered for t = s and φ = 0 by C. M. Bender et al [12][14] [48][37] [52] (see also Z. Ahmed [24]) and later for t = s and φ = 0 by A. Das and L. Greenwood [53][54] and A. Ghatak and B. Mandal [55] (with t, s, r, θ and φ being real-valued parameters):…”

Section: Appendix Bmentioning

confidence: 99%

“…The metric for a two-dimensional Hamilton operator proposed by C. M. Bender et alAppendix B contains our results for the metric of the following asymmetric two-dimensional Hamilton operator H (with t, s, r, θ and φ being realvalued parameters) considered for t = s and φ = 0 by A. Das and L. Greenwood[53][54] and A. Ghatak and B. Mandal[55], i. e., H = r e +i θ s e +i φ t e −i φ r e −i θ ,…”

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Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices

Kleefeld

2021

Preprint

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Physics needs new ideas. But to have a new idea is a very difficult task: it does not mean to write a few lines in a paper. If you want to be the father of a new idea, you should fully devote your intellectual energy to understand all details and to work out the best way in order to put the new idea under experimental test.This can take years of work. You should not give up. If you believe that your new idea is a good one, you should work hard and never be afraid to reach the point where a new-comer can, with little effort, find the result you have been working, for so many years, to get.The new-comer can never take away from you the privilege of having been the first to open a new field with your intelligence, imagination and hard work. Do not be afraid to encourage others to pursue your dream. If it becomes real, the community will never forget that you have been the first to open the field." (Isidor Isaac Rabi, 1972 [1])

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Section: Appendix Bmentioning

confidence: 99%

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confidence: 99%

Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices

Kleefeld

2021

Preprint

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“…It is not so straightforward to obtain an exact expression of the metric, in fact, there are only a limited number of articles producing exact forms, see; for instance [79][80][81][82]. However, there are various methods to obtain the same, for example, using the perturbation theory, spectral theory [83,84], Moyal product [85], etc.…”

Section: Pseudo-hermiticitymentioning

confidence: 99%

An introductory review on resource theories of generalized nonclassical light

Dey

2021

Preprint

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Quantum resource theory is perhaps the most revolutionary framework that quantum physics has ever experienced. It plays vigorous roles in unifying the quantification methods of a requisite quantum effect as wells as in identifying protocols that optimize its usefulness in a given application in areas ranging from quantum information to computation. Moreover, the resource theories have transmuted radical quantum phenomena like coherence, nonclassicality and entanglement from being just intriguing to being helpful in executing realistic thoughts. A general quantum resource theoretical framework relies on the method of categorization of all possible quantum states into two sets, namely, the free set and the resource set. Associated with the set of free states there is a number of free quantum operations emerging from the natural constraints attributed to the corresponding physical system. Then, the task of quantum resource theory is to discover possible aspects arising from the restricted set of operations as resources. Along with the rapid growth of various resource theories corresponding to standard harmonic oscillator quantum optical states, significant advancement has been expedited along the same direction for generalized quantum optical states. Generalized quantum optical framework strives to bring in several prosperous contemporary ideas including nonlinearity, PT -symmetric non-Hermitian theories, q-deformed bosonic systems, etc., to accomplish similar but elevated objectives of the standard quantum optics and information theories. In this article, we review the developments of nonclassical resource theories of different generalized quantum optical states and their usefulness in the context of quantum information theories.

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“…In practical terms, however, there are very few examples [150,151] where one can compute them in an exact manner, as for example; see, [86,152] for an exact form of the metric which was derived in the context of Euclidean Lie algebraic Hamiltonians. However, there are many other methods such as spectral theory, perturbation technique [141,153], Moyal product approach [154] etc., which one may follow for the construction of the metric operator.…”

Section: Pseudo-hermiticitymentioning

confidence: 99%

Coherent States and Their Applications

2018

Springer Proceedings in Physics

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It was at the dawn of the historical developments of quantum mechanics when Schrödinger, Kennard and Darwin proposed an interesting type of Gaussian wave packets, which do not spread out while evolving in time. Originally, these wave packets are the prototypes of the renowned discovery, which are familiar as "coherent states" today. Coherent states are inevitable in the study of almost all areas of modern science, and the rate of progress of the subject is astonishing nowadays. Nonclassical states constitute one of the distinguished branches of coherent states having applications in various subjects including quantum information processing, quantum optics, quantum superselection principles and mathematical physics. On the other hand, the compelling advancements of non-Hermitian systems and related areas have been appealing, which became popular with the seminal paper by Bender and Boettcher in 1998. The subject of non-Hermitian Hamiltonian systems possessing real eigenvalues are exploding day by day and combining with almost all other subjects rapidly, in particular, in the areas of quantum optics, lasers and condensed matter systems, where one finds ample successful experiments for the proposed theory. For this reason, the study of coherent states for non-Hermitian systems have been very important. In this article, we review the recent developments of coherent and nonclassical states for such systems and discuss their applications and usefulness in different contexts of physics. In addition, since the systems considered here originate from the broader context of the study of minimal uncertainty relations, our review is also of interest to the mathematical physics community.

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Comparison of Different Approaches of Finding the Positive Definite Metric in Pseudo-Hermitian Theories

Cited by 12 publications

References 57 publications

Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices

Identification of the metric for diagonalizable (anti-)pseudo-Hermitian Hamilton operators represented by two-dimensional matrices

An introductory review on resource theories of generalized nonclassical light

Coherent States and Their Applications

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