Induced transitions in non-Hermitian spin-boson models with time-dependent boundaries

Andreas Fring; Marta Reboiro

arxiv: 2605.20019 · v1 · pith:Y67JQZN3new · submitted 2026-05-19 · 🪐 quant-ph · math-ph· math.MP

Induced transitions in non-Hermitian spin-boson models with time-dependent boundaries

Andreas Fring , Marta Reboiro This is my paper

Pith reviewed 2026-05-20 05:16 UTC · model grok-4.3

classification 🪐 quant-ph math-phmath.MP

keywords non-Hermitian quantum mechanicsspin-boson modeltime-dependent boundariesDyson mapsqueezing transformationtransition amplitudescoherent interference

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The pith

Varying the non-Hermitian parameter during time-dependent boundary motion enables coherent control of transitions differing by two bosonic quanta.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines a non-Hermitian extension of the spin-boson Hamiltonian with complex couplings and time-dependent boundaries. A time-dependent Dyson map including a squeezing transformation converts the model, inside a bounded regime, into a Hermitian partner with real instantaneous energies while representing the moving boundaries inside a fixed domain. Fixed boundaries conserve a quantity that blocks transitions between sectors differing by two bosonic quanta, but the motion opens those channels. Closed protocols with constant parameters produce a vanishing first-order transition amplitude because constant squeezing remains unitary, yet letting the non-Hermitian parameter vary during the motion changes the instantaneous dressed basis and creates controllable interference that can suppress or enhance the transitions.

Core claim

A time-dependent Dyson map containing a squeezing transformation maps the non-Hermitian spin-boson model with moving boundaries, in an admissible bounded regime, to a Hermitian Hamiltonian with real instantaneous energy spectrum. The boundary motion opens transition channels between sectors differing by two bosonic quanta that are forbidden when boundaries are fixed. For closed protocols with constant background parameters the first-order integrated transition amplitude vanishes, while varying the non-Hermitian parameter during the motion changes the dressed basis and permits suppression or enhancement of transitions by coherent interference.

What carries the argument

The time-dependent Dyson map with squeezing transformation, which converts the non-Hermitian model to a Hermitian partner and interprets the squeezing as a dilatation term representing moving boundaries in a fixed domain.

Load-bearing premise

The model remains inside an admissible bounded regime where a time-dependent Dyson map containing a squeezing transformation exists and produces a Hermitian partner with real instantaneous energy spectrum.

What would settle it

Measure or compute the first-order integrated transition amplitude for a closed boundary protocol with constant non-Hermitian parameter and verify that it vanishes exactly, or for a protocol where the parameter varies check whether the amplitude exhibits interference-driven suppression or enhancement matching the changed dressed basis.

read the original abstract

We study a time-dependent non-Hermitian extension of the Sch\"utte-Da~Provid\^encia spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map containing a squeezing transformation maps the model, in an admissible bounded regime, to a Hermitian Hamiltonian with real instantaneous energy spectrum. The squeezing contribution generates a dilatation term allowing the Hermitian partner to be interpreted as a fixed-domain representation of a system with moving boundaries. While the fixed-boundary Hermitian model conserves $Q=N-S_0$ and forbids transitions between sectors differing by two bosonic quanta, the boundary motion opens such channels. For closed boundary protocols with constant background parameters the first-order integrated transition amplitude vanishes, reflecting the unitary nature of constant squeezing. Nontrivial transition control arises when the non-Hermitian parameter varies during the boundary motion, changing the dressed basis and allowing boundary-induced transitions to be suppressed or enhanced by coherent interference.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows how varying the non-Hermitian parameter during closed boundary motion produces controllable interference in otherwise forbidden transitions, but only if the time-dependent Dyson map stays inside its admissible regime the whole time.

read the letter

The main point is that this work finds a concrete way to turn boundary motion into a tunable transition mechanism in a non-Hermitian spin-boson model. By letting the non-Hermitian parameter change while the boundaries follow a closed protocol, the changing dressed basis creates interference that can suppress or enhance the amplitude for transitions that differ by two bosonic quanta. In the constant-parameter case the amplitude vanishes, as expected from unitary squeezing, but the variation opens a control knob. That specific protocol looks like the genuinely new element beyond the static or fixed-boundary cases in the literature they cite. The mapping itself is handled by a time-dependent Dyson map that includes squeezing; the squeezing term supplies a dilatation that lets them read the Hermitian partner as a fixed-domain version of a moving-boundary problem. This gives a clean physical picture and keeps the instantaneous spectrum real inside the stated admissible regime. The construction is explicit enough in outline that the claims are checkable once the equations are written down. The soft spot is exactly the one the stress-test flags: whether the admissible regime survives when both the non-Hermitian parameter and the boundary motion are active at once. The squeezing-induced corrections could in principle push eigenvalues off the real axis or violate boundedness at intermediate times, and the abstract only asserts that the regime remains non-empty without showing the explicit bounds or numerical checks. If the full derivations contain a clear proof that the map stays valid throughout the protocol, the concern is minor; if they are only sketched, it needs tightening. This is niche work aimed at people already working on time-dependent non-Hermitian systems and exact mappings. A reader who cares about boundary effects or interference control in PT-symmetric or open quantum models will get something concrete out of it. It is solid enough on its own terms to deserve a serious referee, provided the regime question is addressed directly in revision.

Referee Report

2 major / 2 minor

Summary. The paper studies a time-dependent non-Hermitian extension of the Schütte-Da Providência spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map containing a squeezing transformation is constructed to map the model, in an admissible bounded regime, to a Hermitian Hamiltonian possessing a real instantaneous energy spectrum. The squeezing term generates a dilatation that permits interpreting the Hermitian partner as a fixed-domain representation of a system with moving boundaries. Boundary motion opens transition channels between sectors differing by two bosonic quanta (forbidden when boundaries are fixed, where Q = N - S_0 is conserved). For closed boundary protocols with constant background parameters the first-order integrated transition amplitude vanishes, consistent with unitarity of constant squeezing. Nontrivial transition control is obtained by varying the non-Hermitian parameter during boundary motion, which changes the dressed basis and permits suppression or enhancement of boundary-induced transitions via coherent interference.

Significance. If the admissible bounded regime remains non-empty and the time-dependent Dyson map with squeezing continues to produce a Hermitian partner with real spectrum throughout the protocol, the work supplies a concrete mechanism for interference-based control of transitions in non-Hermitian systems with time-dependent boundaries. The explicit vanishing of the first-order amplitude for constant-parameter closed protocols serves as an internal consistency check, and the mapping between non-Hermitian dynamics and moving-boundary Hermitian dynamics is a useful interpretive bridge.

major comments (2)

[Abstract and Dyson-map construction] The central claim of nontrivial transition control via coherent interference rests on the continued existence of the time-dependent Dyson map (including its squeezing component) and the preservation of a real instantaneous spectrum when the non-Hermitian parameter is varied jointly with the boundary motion. The abstract invokes an 'admissible bounded regime' but supplies no explicit construction, bounds, or verification that this regime remains non-empty under simultaneous variation; the squeezing-induced dilatation term could generate time-dependent corrections that drive eigenvalues off the real axis or violate boundedness.
[Transition-amplitude calculation] The statement that the first-order integrated transition amplitude vanishes for constant background parameters is presented as a direct consequence of the unitary nature of constant squeezing. Without the explicit form of the time-dependent Dyson map, the interaction-picture perturbation, or the integration limits for the closed protocol, it is not possible to confirm that this cancellation holds beyond the constant-squeezing case and is not an artifact of the chosen representation.

minor comments (2)

[Model definition] Define the operator Q = N - S_0 and state its commutation relations with the fixed-boundary Hamiltonian explicitly so that conservation and the opening of ΔQ = ±2 channels are immediately visible.
[Numerical results] If numerical illustrations of transition probabilities are included, add a comparison to the analytic first-order result for the constant-parameter case to demonstrate consistency.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments raise important points about the explicit characterization of the admissible regime and the details of the transition amplitude calculation. We address each major comment below and indicate the revisions planned for the next version of the manuscript.

read point-by-point responses

Referee: [Abstract and Dyson-map construction] The central claim of nontrivial transition control via coherent interference rests on the continued existence of the time-dependent Dyson map (including its squeezing component) and the preservation of a real instantaneous spectrum when the non-Hermitian parameter is varied jointly with the boundary motion. The abstract invokes an 'admissible bounded regime' but supplies no explicit construction, bounds, or verification that this regime remains non-empty under simultaneous variation; the squeezing-induced dilatation term could generate time-dependent corrections that drive eigenvalues off the real axis or violate boundedness.

Authors: We appreciate the referee drawing attention to the need for greater explicitness. The admissible bounded regime is defined in the manuscript through the requirement that the Dyson map yields a positive-definite metric and a Hermitian partner with real spectrum; this imposes bounds on the imaginary part of the complex couplings relative to the real part. For the time-dependent case with joint variation of the non-Hermitian parameter and boundary motion, the construction ensures the instantaneous map remains valid provided the parameters do not exit this regime. To strengthen the presentation, the revised manuscript will include an explicit statement of these bounds together with a verification that the protocols examined keep the system inside the admissible regime, confirming that the squeezing dilatation does not drive the spectrum off the real axis. revision: yes
Referee: [Transition-amplitude calculation] The statement that the first-order integrated transition amplitude vanishes for constant background parameters is presented as a direct consequence of the unitary nature of constant squeezing. Without the explicit form of the time-dependent Dyson map, the interaction-picture perturbation, or the integration limits for the closed protocol, it is not possible to confirm that this cancellation holds beyond the constant-squeezing case and is not an artifact of the chosen representation.

Authors: We agree that additional explicit detail will make the argument more transparent. The vanishing of the first-order amplitude for constant parameters follows directly from the unitarity of the time-independent squeezing operator, which produces a global phase factor whose integral over the closed protocol is zero. In the revised manuscript we will provide the explicit form of the (time-dependent) Dyson map, the interaction-picture representation of the perturbation, and the precise integration limits used for the closed boundary protocols, thereby confirming the cancellation explicitly rather than relying solely on the unitarity argument. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on explicit map construction

full rationale

The paper constructs a time-dependent Dyson map containing a squeezing transformation that maps the non-Hermitian extension to a Hermitian partner with real instantaneous spectrum inside a stated admissible bounded regime. The dilatation term from squeezing is then used to reinterpret the partner as a fixed-domain model of moving boundaries, after which transition amplitudes are computed for constant versus varying non-Hermitian parameters. This chain is a forward mathematical construction rather than a reduction of outputs to inputs by definition or fitting; the vanishing first-order amplitude for constant squeezing follows from unitarity, and the interference effect when the non-Hermitian parameter varies follows from the changed dressed basis. No self-citation is shown to be load-bearing, no parameter is fitted and renamed as a prediction, and the admissible regime is posited as a precondition rather than derived tautologically from the final transition result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim depends on the existence of a time-dependent Dyson map in a bounded regime and on the unitary evolution of the resulting Hermitian partner; no new physical entities are introduced.

free parameters (1)

non-Hermitian parameter
This parameter is varied during the boundary protocol to produce the interference effect; its explicit functional form is not fixed by the abstract.

axioms (1)

domain assumption A time-dependent Dyson map with squeezing exists and maps the non-Hermitian Hamiltonian to a Hermitian operator with real instantaneous spectrum inside an admissible regime.
Invoked to justify the mapping and the fixed-domain interpretation of moving boundaries.

pith-pipeline@v0.9.0 · 5689 in / 1388 out tokens · 68961 ms · 2026-05-20T05:16:17.544795+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages

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P. K. Ghosh, Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry, J. of Phys. A: Math. and Theor. 38(33), 7313–7323 (2005). 15 Induced transitions in non-Hermitian spin-boson models with time-dependent boundaries

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[1] [1]

El-Ganainy, K

R. El-Ganainy, K. G. Makris, M. Khajavikhan, Z. H. Musslimani, S. Rotter, and D. N. Christodoulides, Non-Hermitian physics and PT symmetry, Nat. Phys.14(1), 11–19 (2018)

work page 2018

[2] [2]

Ashida, Z

Y. Ashida, Z. Gong, and M. Ueda, Non-Hermitian physics, Adv. Phys.69(3), 249–435 (2020)

work page 2020

[3] [3]

E. J. Bergholtz, J. C. Budich, and F. K. Kunst, Exceptional topology of non-Hermitian systems, Rev. Mod. Phys.93(1), 015005 (2021)

work page 2021

[4] [4]

Zhang, T

X. Zhang, T. Zhang, M.-H. Lu, and Y.-F. Chen, A review on non-Hermitian skin effect, Adv. Phys.: X7(1), 2109431 (2022)

work page 2022

[5] [5]

C. M. Bender and S. Boettcher, Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry, Phys. Rev. Lett.80, 5243–5246 (1998)

work page 1998

[6] [6]

C. M. Bender, Making sense of non-Hermitian Hamiltonians, Rept. Prog. Phys.70, 947–1018 (2007). 14 Induced transitions in non-Hermitian spin-boson models with time-dependent boundaries

work page 2007

[7] [7]

Mostafazadeh, Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J

A. Mostafazadeh, Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian, J. Maths. Phys.43, 202–212 (2002)

work page 2002

[8] [8]

Mostafazadeh, Pseudo-Hermitian Representation of Quantum Mechanics, Int

A. Mostafazadeh, Pseudo-Hermitian Representation of Quantum Mechanics, Int. J. Geom. Meth. Mod. Phys.7, 1191–1306 (2010)

work page 2010

[9] [9]

F. G. Scholtz, H. B. Geyer, and F. Hahne, Quasi-Hermitian Operators in Quantum Mechanics and the Variational Principle, Ann. Phys.213, 74–101 (1992)

work page 1992

[10] [10]

Fring and M

A. Fring and M. H. Y. Moussa, Unitary quantum evolution for time-dependent quasi-Hermitian systems with nonobservable Hamiltonians, Phys. Rev. A93(4), 042114 (2016)

work page 2016

[11] [11]

Fring, An introduction to PT-symmetric quantum mechanics-time-dependent systems, J

A. Fring, An introduction to PT-symmetric quantum mechanics-time-dependent systems, J. Phys.: Conf. Ser.2448(1), 012002 (2023)

work page 2023

[12] [12]

Sch¨ utte and J

D. Sch¨ utte and J. Da Providencia, A solvable model of boson condensation, Nucl. Phys. A 282(3), 518–532 (1977)

work page 1977

[13] [13]

Civitarese and M

O. Civitarese and M. Reboiro, Boson mapping at finite temperature: An application to the thermo field dynamics, Phys. Rev. C60, 034302–034302 (1999)

work page 1999

[14] [14]

Reboiro and D

M. Reboiro and D. Tielas, Quantum work from a pseudo-Hermitian Hamiltonian, Quantum Rep.4(4), 589–603 (2022)

work page 2022

[15] [15]

Fring and T

A. Fring and T. Taira, Non-Hermitian Quantum Fermi Accelerator, Phys. Rev. A108(1), 012222 (2023)

work page 2023

[16] [16]

Doescher and M

S. Doescher and M. Rice, Infinite square-well potential with a moving wall, Am. J. Phys. 37(12), 1246–1249 (1969)

work page 1969

[17] [17]

Law, Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium, Phys

C. Law, Effective Hamiltonian for the radiation in a cavity with a moving mirror and a time-varying dielectric medium, Phys. Rev. A49(1), 433 (1994)

work page 1994

[18] [18]

Dodonov, Current status of the dynamical Casimir effect, Phys

V. Dodonov, Current status of the dynamical Casimir effect, Phys. Scr.82(3), 038105 (2010)

work page 2010

[19] [19]

Longhi and G

S. Longhi and G. Della Valle, Non-Hermitian time-dependent perturbation theory: Asymmetric transitions and transitionless interactions, Ann. Phys.385, 744–756 (2017)

work page 2017

[20] [20]

E. T. Jaynes and F. W. Cummings, Comparison of quantum and semiclassical radiation theories with application to the beam maser, Proc. IEEE51(1), 89–109 (1963)

work page 1963

[21] [21]

Frith, Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians, J

T. Frith, Exotic entanglement for non-Hermitian Jaynes–Cummings Hamiltonians, J. of Phys. A: Math. and Theor.53(48), 485303 (2020)

work page 2020

[22] [22]

Tavis and F

M. Tavis and F. W. Cummings, Exact solution for an N-molecule—radiation-field Hamiltonian, Phys. Rev.170(2), 379 (1968)

work page 1968

[23] [23]

R. H. Dicke, Coherence in spontaneous radiation processes, Phys. Rev.93(1), 99 (1954)

work page 1954

[24] [24]

P. K. Ghosh, Exactly solvable non-Hermitian Jaynes–Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry, J. of Phys. A: Math. and Theor. 38(33), 7313–7323 (2005). 15 Induced transitions in non-Hermitian spin-boson models with time-dependent boundaries

work page 2005

[25] [25]

Exceptional Points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian,

F. Bagarello, F. Gargano, M. Lattuca, R. Passante, L. Rizzuto, and S. Spagnolo, “Exceptional Points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian,” in Non-Hermitian Hamiltonians in Quantum Physics, pp. 83–95, Springer, 2016

work page 2016

[26] [26]

Zhang, Z

G.-Q. Zhang, Z. Chen, and J. You, Experimentally accessible quantum phase transition in a non-Hermitian Tavis-Cummings model engineered with two drive fields, Physi. Rev. A 102(3), 032202 (2020)

work page 2020

[27] [27]

N. Liu, S. Huang, and J.-Q. Liang, Macroscopic quantum states in Dicke model of PT-symmetric non-Hermitian Hamiltonian and superradiant phase with imaginary atomic population, Res. Phys.40, 105813 (2022). 16

work page 2022