Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

Subramanyan, Varsha; Hegde, Suraj S.; Vishveshwara, Smitha; Bradlyn, Barry

doi:10.1016/j.aop.2021.168470

“…The results of this work can be also applied in quantum metrology for precise measurements of ω and Ω [50][51][52] as well as for the preparation of squeezed states, simulations of the inflation of the early Universe [53][54][55][56], the Unruh effect [57,58], Hawking radiation [59], quantum chaos [60,61], and potentially to study many other aspects of physics in which the inverted harmonic oscillator has been harnessed as an underlying mechanism (see Ref. [20] for the recent review).…”

Section: Discussionmentioning

confidence: 99%

“…In this work, we show that for a limited and quantifiable time the dynamics after a quench can be mapped to dynamics of a simple inverted harmonic oscillator [19,20]. Our model is based on an effective Hamiltonian that cannot be used to fully describe the equilibrium states [21,22].…”

Section: Introductionmentioning

confidence: 97%

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

Gietka,

Busch

2021

Preprint

0

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We show how the dynamics of the Dicke model after a quench from the ground-state configuration of the normal phase into the superradiant phase can be described for a limited time by a simple inverted harmonic oscillator model and that this limited time approaches infinity in the thermodynamic limit. Although we specifically discuss the Dicke model, the presented mechanism can be also used to describe dynamical quantum phase transitions in other systems and opens a new avenue in simulations of physical phenomena associated with an inverted harmonic oscillator.

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“…The two coupled inverted quantum harmonic oscillator [69][70][71] can be described by the Hamiltonian H which is the sum of the free Hamiltonian of both the inverted quantum harmonic oscillators and the interaction Hamiltonian H int which depends on the type interaction between them and the coupling constant K accounts for the strength of the interaction between the two coupled inverted quantum harmonic oscillators:…”

Section: B the Two Coupled Inverted Harmonic Oscillatormentioning

confidence: 99%

“…Heisenberg representation for the two coupled scalar fields in de Sitter background space and using the factorized representation of the unitary time evolution operator introduced in the Eq (71), the expression for the annihilation operator for field 1 can be written at any arbitrary time scale as:…”

Section: Are the Annihilation And Creation Operators In Time Dependentmentioning

confidence: 99%

“…Now for operator b 2 , we will apply the same factorized representation of the unitary time evolution operator mentioned in the Eq (71), the expression for the annihila-tion operator for field 2 can be written at any arbitrary time scale as Eq(76). For the creation operator b † 2 of field 2, one can take the conjugate of Eq(76) or (77).…”

Section: Are the Annihilation And Creation Operators In Time Dependentmentioning

confidence: 99%

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Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system

Choudhury¹,

Panda²,

Pandey³

et al. 2022

Preprint

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In this paper we study the application of four-mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four-mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time-dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

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Four‐mode Squeezed States in de Sitter Space: A Study With Two Field Interacting Quantum System

Choudhury

¹

,

Panda

²

,

Pandey

³

et al. 2022

Fortschritte der Physik

View full text Add to dashboard Cite

In this paper we study the application of four-mode squeezed states in the cosmological context, studying two weakly coupled scalar fields in the planar patch of the de Sitter space. We construct the four-mode squeezed state formalism and connect this concept with the Hamiltonian of the two coupled inverted harmonic oscillators having a time-dependent effective frequency in the planar patch of the de Sitter space. Further, the corresponding evolution operator for the quantum Euclidean vacuum state has been constructed, which captures its dynamics. Using the Heisenberg picture coupled differential equations describing the time evolution for all squeezing parameters (amplitude, phase and angle) have been obtained, for the weakly coupled two scalar field model. With the help of these evolutions for the coupled system, we simulate the dynamics of the squeezing parameters in terms of conformal time. From our analysis, we observe interesting dynamics, which helps us to explore various underlying physical implications of the weakly coupled two scalar field system in the planar patch of the de Sitter cosmological background.

show abstract

Physics of the Inverted Harmonic Oscillator: From the lowest Landau level to event horizons

Cited by 38 publications

References 130 publications

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

Inverted harmonic oscillator dynamics of the nonequilibrium phase transition in the Dicke model

Four-mode squeezed states in de Sitter space: A study with two field interacting quantum system

Four‐mode Squeezed States in de Sitter Space: A Study With Two Field Interacting Quantum System

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