Embedding, simulation and consistency of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric quantum theory

Huang, Minyi; Kumar, Asutosh; Wu, Junde

doi:10.1016/j.physleta.2018.06.047

Cited by 20 publications

(31 citation statements)

References 29 publications

(91 reference statements)

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“…Note that (3) implies that η > 0, that is, η is positive definite. It can be proved that the solutions to (3) and ( 5) exist if and only if H is unbroken PT -symmetric [9]. On the other hand, if we relax the condition only considering (5), then the η also exists for any broken PTsymmetric Hamiltonian.…”

Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

“…However, in this case, η is indefinite (has negative eigenvalues and cannot be used for dilation). A detailed discussion of the time independent dilation prob-lem can be found in in [7][8][9]. To simulate the broken PT -symmetric systems, researchers usually consider the time dependent case, namely (4).…”

Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

“…Finite dimensional PT -symmetric Hamiltonians, as well as their metric operators, have some special structures [9,14]. As an example, for the Hamiltonian H in (1) and its certain metric operator η, there exist an invertible matrix such that…”

Section: The Structure Of Finite Dimensional Pt -Symmetric Systemsmentioning

confidence: 99%

“…Utilizing the η-inner product, PT -symmetric quantum theory was generalized to the pseudo-Hermitian theory [6]. Despite a theoretical concept, η-inner product was shown to be tightly linked to the experimental realization of PT -symmetric systems [7][8][9]. Indeed, it is not only the key concept of pseudo-Hermitian theory but also a mark of distinction between different types of PT -symmetric systems.…”

Section: Introductionmentioning

confidence: 99%

“…In the case of unbroken PT -symmetry, the η-inner product can be either definite or indefinite. On the other hand, the η-inner product of broken PT -symmetry can only be indefinite [9]. This paper focuses on the discussion of η-inner product, especially on the distinction between the η-inner products of broken and unbroken PT -symmetric systems.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

Huang

Zhang

2021

Int J Theor Phys

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In this paper, we consider a typical continuous two dimensional PT -symmetric Hamiltonian and propose two different approaches to quantitatively show the difference between the η-inner products. Despite the continuity of Hamiltonian, the η-inner product is not continuous in some sense. It is shown that the difference between the η-inner products of broken and unbroken PT -symmetry is lower bounded. Moreover, such a property can lead to some uncertainty relation.

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Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

Section: The Concepts Of Metric Operator and Dilationmentioning

confidence: 99%

Section: The Structure Of Finite Dimensional Pt -Symmetric Systemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

Huang

Zhang

2021

Int J Theor Phys

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Parity‐Time Symmetry in Non‐Hermitian Complex Optical Media

et al. 2019

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The explorations of the quantum-inspired symmetries in optical and photonic systems have witnessed immense research interests both fundamentally and technologically in a wide range of subjects of physics and engineering. One of the principal emerging fields in this context is non-Hermitian physics based on parity-time symmetry, originally proposed in the studies pertaining to quantum mechanics and quantum field theory, recently ramified into diverse set of areas, particularly in optics and photonics. The intriguing physical effects enabled by non-Hermitian physics and PT symmetry have enhanced significant applications prospects and engineering of novel materials. In addition, it has observed increasing research interests in many emerging directions beyond optics and photonics. This Review paper attempts to bring together the state of the art developments in the field of complex non-Hermitian physics based on PT symmetry in various physical settings along with elucidating key concepts and background and a detailed perspective on new emerging directions. It can be anticipated that this trendy field of interest can be indispensable in providing new perspectives in maneuvering the flow of light in the diverse physical platforms in optics, photonics, condensed matter, opto-electronics and beyond, and offer distinctive applications prospects in novel functional materials.

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Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

Singh,

Banerjee

2023

J. Phys. A: Math. Theor.

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The problem of how measurement in quantum mechanics takes place has existed since its formulation. Von Neumann proposed a scheme where he treated measurement as a two-part process— a unitary evolution in the full system-ancilla space and then a projection onto one of the pointer states of the ancilla (representing the ‘collapse’ of the wavefunction). The Lindblad master equation, which has been extensively used to explain dissipative quantum phenomena in the presence of an environment, can effectively describe the first part of the von Neumann measurement scheme when the jump operators in the master equation are Hermitian. We have proposed a non-Hermitian Hamiltonian formalism to emulate the first part of the von Neumann measurement scheme. We have used the embedding protocol to dilate a non-Hermitian Hamiltonian that governs the dynamics in the system subspace into a higher-dimensional Hermitian Hamiltonian that evolves the full space unitarily. We have obtained the various constraints and the required dimensionality of the ancilla Hilbert space in order to achieve the required embedding. Using this particular embedding and a specific projection operator, one obtains non-Hermitian dynamics in the system subspace that closely follow the Lindblad master equation. This work lends a new perspective to the measurement problem by employing non-Hermitian Hamiltonians.

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Embedding, simulation and consistency ofPT-symmetric quantum theory

Cited by 20 publications

References 29 publications

To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

To Quantify the Difference of η-Inner Products in $\mathcal {P}\mathcal {T}$-Symmetric Theory

Parity‐Time Symmetry in Non‐Hermitian Complex Optical Media

Embedding of a non-Hermitian Hamiltonian to emulate the von Neumann measurement scheme

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