Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides

Zloshchastiev, Konstantin G.

doi:10.1103/physrevb.94.115136

Cited by 17 publications

(22 citation statements)

References 53 publications

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“…Around the year 2006, many Schrödinger equations describing the quantum-mechanical models were revealed to be mathematically-equivalent to Maxwell equations in media [26,27], see also more recent works [28,29]. This opened a way towards a natural, phenomenologically-motivated introduction of nonlinear interaction terms and, in particular, towards the nonlinear Schrödinger equations.…”

Section: The Turn Of Attention To Classical Opticsmentioning

confidence: 98%

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

2017

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Schrödinger equations with non-Hermitian, but P T -symmetric quantum potentials V(x) found, recently, a new field of applicability in classical optics. The potential acquired there a new physical role of an "anomalous" refraction index. This turned attention to the nonlinear Schrödinger equations in which the interaction term becomes state-dependent, V(x) → W(ψ(x), x). Here, the state-dependence in W(ψ(x), x) is assumed logarithmic, and some of the necessary mathematical assumptions, as well as some of the potential phenomenological consequences of this choice are described. Firstly, an elementary single-channel version of the nonlinear logarithmic model is outlined in which the complex self-interaction W(ψ(x), x) is regularized via a deformation of the real line of x into a self-consistently constructed complex contour C. The new role played by P T -symmetry is revealed. Secondly, the regularization is sought for a multiplet of equations, coupled via the same nonlinear self-interaction coupling of channels. The resulting mathematical structures are shown to extend the existing range of physics covered by the logarithmic Schrödinger equations.

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Section: The Turn Of Attention To Classical Opticsmentioning

confidence: 98%

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

2017

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“…Since probability non-conserving quantum systems are open quantum systems [ 14 ], it is natural to formulate NHQM in terms of the density matrix [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Typically, a non-Hermitian Hamiltonian is either derived by means of the Feshbach formalism [ 23 , 24 ] or it is postulated as an ansatz (see [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]). It is remarkable that there is a third possibility according to which a non-Hermitian Hamiltonian may arise from stroboscopic measurements performed on an ancilla-subsystem added to a quantum system, a very interesting process capable of generating entanglement [ 25 ].…”

Section: Introductionmentioning

confidence: 99%

“…Given a non-Hermitian Hamiltonian and assuming that the Schrödinger equation is still valid, one derives a probability non-conserving equation of motion for the density matrix of the system [ 25 ]. However, in order to meet the need of establishing a proper quantum statistical theory, this non-Hermitian equation of motion for the density matrix is generalized into a non linear-one [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ]. Essentially, this is the origin of the difference between the linear approach of [ 10 , 11 , 12 ] and the non-linear approach of [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 ].…”

Section: Introductionmentioning

confidence: 99%

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

Grimaldi

Sergi

Messina

2021

Entropy

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This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states (∼10) and many more classical modes or atomic particles (∼103−105) is highlighted.

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“…Hence, the projection operator formalism [ 4 , 5 , 6 ] and non-Hermitian Hamiltonians provides an effective way to describe decaying states. Non-Hermitian Hamiltonians can also be postulated on the basis of physical considerations [ 8 , 9 , 10 , 11 , 12 ], in order to describe gain or loss of probability. Dynamics in terms of non-Hermitian Hamiltonians have been investigated for quantum [ 13 ] and quantum-classical systems [ 14 ], adopting phase space representation quantum mechanics.…”

Section: Introductionmentioning

confidence: 99%

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

Grimaudo

Messina

Sergi

et al. 2020

Entropy

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In contrast to classical systems, actual implementation of non-Hermitian Hamiltonian dynamics for quantum systems is a challenge because the processes of energy gain and dissipation are based on the underlying Hermitian system–environment dynamics, which are trace preserving. Recently, a scheme for engineering non-Hermitian Hamiltonians as a result of repetitive measurements on an ancillary qubit has been proposed. The induced conditional dynamics of the main system is described by the effective non-Hermitian Hamiltonian arising from the procedure. In this paper, we demonstrate the effectiveness of such a protocol by applying it to physically relevant multi-spin models, showing that the effective non-Hermitian Hamiltonian drives the system to a maximally entangled stationary state. In addition, we report a new recipe to construct a physical scenario where the quantum dynamics of a physical system represented by a given non-Hermitian Hamiltonian model may be simulated. The physical implications and the broad scope potential applications of such a scheme are highlighted.

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Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides

Cited by 17 publications

References 53 publications

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature

Two-Qubit Entanglement Generation through Non-Hermitian Hamiltonians Induced by Repeated Measurements on an Ancilla

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