The Heisenberg–Robertson uncertainty relation is a standard tool in quantum mechanics, but its use in non-Hermitian settings is not straightforward, especially in regimes with complex spectra and exceptional points. In this context, we study uncertainty relations for pseudo-Hermitian, in particular PT-symmetric Hamiltonians by introducing a metric operator in all spectral regimes. As a simple and widely used test case, we focus on a non-Hermitian two-level toy model with balanced gain and loss, which shows the transition from an exact PT-symmetric phase to a symmetry-broken phase through an exceptional point.

The chosen method is based on the explicit construction, in each regime, of a positive-definite metric operator that induces a modified inner product and defines the physical expectation values and variances. On this basis, we derive generalized Heisenberg–Robertson uncertainty relations for selected observables of the two-level model and compute their behavior in the exact, broken, and exceptional-point regions. In parallel, we construct a description in terms of a Lindblad master equation for the corresponding open two-level system and use it as a reference to compare with the non-Hermitian effective dynamics.

We find that the metric-based formulation restores an uncertainty relation with the same formal structure as in the Hermitian case, whereas the direct use of the standard inner product can lead to ill-defined quantities, in particular in the symmetry-broken phase and at the exceptional point. The comparison with Lindblad dynamics shows agreement between the metric-based description and features such as PT-symmetry breaking and decoherence. These results indicate that, even for a two-level toy model, an appropriate metric is necessary to obtain consistent uncertainty bounds and dynamical predictions from pseudo-Hermitian Hamiltonians.

Our research explores the sensitivity of satellite constellations to fluctuations in the quantum gravitational field, with the aim of quantifying their potential impact on critical operations and precision measurements. The main objective is to quantify the potential impact of hypothetical quantum effects on the precise orbital dynamics of satellite constellations. The methods employed will involve the development of a sophisticated computational model using MATLAB. Our model will simulate the trajectories of various satellite constellation configurations in two distinct gravitational frameworks: one based on classical general relativity and the other incorporating theoretical models of quantum gravitational fluctuations. The main task is to meticulously analyze and compare the resulting differences in key orbital parameters, including position, velocity, and orbital period, between these two scenarios. This comparative analysis is crucial in determining whether the minute stochastic perturbations resulting from quantum gravity could accumulate over time and measurably affect the performance and objectives of current and future high-precision satellite missions, such as those related to Earth observation, global navigation satellite systems (GNSSs), or space-based gravitational wave detectors. The expected results have provided essential insights into the potential need to integrate quantum gravitational corrections into very high-precision astrodynamics and will contribute significantly to ongoing theoretical and experimental efforts to unify quantum mechanics and general relativity at the macroscopic scale.

In this talk, I will discuss the notion of thermally averaged mean energy of a quantum harmonic oscillator strongly coupled to a heat bath, defined as the expectation value of the bare-system Hamiltonian in the canonical Gibbs state of the composite system, i.e., the system and bath taken together with their interactions. This quantity differs fundamentally from the thermodynamic internal energy obtained from the reduced partition function and provides an alternative perspective on the strong-coupling energetics. Using the Brownian quantum oscillator as a paradigmatic example, I will show how this mean energy can be consistently interpreted within the frameworks of quantum thermodynamics and stochastic energetics.

Based on the fluctuation–dissipation theorem, I will first show how the Lehmann–Kubo representation of the generalized susceptibility allows one to interpret the mean energy as the bare oscillator's energy contained within the dressed eigenmodes of the composite system. I will then show, using the quantum Langevin equation, that the mean energy obeys an exact energy-balance relation consistent with the framework of stochastic energetics, even in the presence of non-Markovian dissipation.

Finally, I will discuss analytical results for Ohmic dissipation with a Drude cutoff and show that, at low temperatures, the thermal part of the mean energy exhibits the same universal power-law behavior as the thermodynamic internal energy. The remaining difference between these two notions of energy is a temperature-independent contribution originating from system-bath correlations, highlighting the persistent role of the environment deep into the quantum regime.

In this study, we analyze the temperature dependence of Exceptional Points (EPs) in a pseudo-Hermitian hybrid model composed of a superconducting flux qubit (SFQ) interacting with an ensemble of nitrogen-vacancy (NV) color centers in diamond [1–2]. This model is relevant not only due to its experimental realizability [1], but also as a representative example of a many-body Hamiltonian exhibiting a nontrivial interplay of distinct physical effects.

The interaction between the NV ensemble and the SFQ is modeled by introducing an asymmetry parameter [2] that modifies the balance between the creation and annihilation processes of NVs coupled to the SFQ. This asymmetry accounts for the presence of impurities within the NV ensemble, such as P1 centers [3].

As reported in [4], temperature effects on the zero-field splitting states of the NV ensemble are negligible below T=200 KT = 200~\mathrm{K}T=200 K. Therefore, we assume that temperature has an insignificant effect on the NV ensemble. This is not the case for the SFQ, as superconductivity is well known to be strongly temperature-dependent.

We investigate how the location of the EPs and the extent of each symmetry phase evolve with temperature by explicitly incorporating the temperature dependence of the superconducting gap in the SFQ . To characterize the system’s evolution and the impact of thermal effects, we analyze several observables, including the survival probability, expectation values of spin components, spin squeezing, and the SU(2) Wigner function. The initial state is prepared as a spin coherent state for the NV ensemble, with the SFQ in its ground state.

Our results show that increasing temperature tends to expand the region of parameter space corresponding to the exact-symmetry phase [5].

[1] X. Zhu et al., Nature 478, 211 (2011).

[2] R. Ramírez, M. Reboiro, and D. Tielas, The European Physical Journal D 74, 193 (2020).

[3] V. Stepanov and S. Takahashi, Phys. Rev. B 94, 024421 (2016).

[4] M. C. Cambria et al., Phys. Rev. B 108, L180102 (2023)

[5] to be published.

One of the canonical approaches to quantum gravity is quantum geometrodynamics. It arises from the quantization of Hamiltonian constraints. This method gives rise to the Wheeler–DeWitt equation, which can be solved in minisuperspace models to obtain the wavefunction of the universe. Despite its long history, this approach still faces fundamental challenges: operator ordering ambiguity, the problem of time, and the lack of a clear probabilistic interpretation remain open issues. In our work, we discuss how studies of entropy may shed some light on these difficulties.

We study a toy model of the Wheeler–DeWitt equation for a Friedmann–Lemaître–Robertson–Walker (FLRW) universe with a non-zero cosmological constant and matter content consisting of a massive scalar field coupled to gravity. We construct the universal wavefunction using a spectral expansion method, which allows us to obtain numerical solutions on the entire domain while avoiding instabilities. This approach enables a detailed analysis of the wavefunction and provides access to both gravitational and matter degrees of freedom without the use of the slow-roll approximation.

Based on the obtained universal wavefunction, we discuss possible entropy measures and their implications, as well as the potential role of matter–geometry entanglement as an indicator of the quantum-to-classical transition. We conclude with a comment on the use of entropy-related quantities as arrows of time.

Rotating traversable wormholes allow the effects of frame-dragging and rotation to be
studied in the absence of event horizons. We develop a quantum field-theoretic treatment of massless scalar perturbations in the rotating Teo spacetime (an exact, stationary,
horizonless, traversable wormhole with two asymptotically flat regions). Using the
Bogoliubov transformation formalism, we construct “in” and “out” mode solutions in the
two asymptotic regions and compute the Bogoliubov coefficients (αωm,βωm) that quantify
mode mixing.
The effective radial potential induced by rotation and frame-dragging forms an
asymmetric scattering barrier. This asymmetry permits an exact analytic evaluation of
reflection and transmission amplitudes via the barrier penetration exponent, yielding
closed-form expressions for the Bogoliubov coefficients, mean particle number,
superradiant amplification, and the two-mode entanglement entropy Sωm as functions of
the rotation parameter a.
Because the spacetime is stationary, particle creation and amplification arise purely from
geometric asymmetry rather than explicit time-dependence. Co-rotating and
counter-rotating modes experience inequivalent scattering, rendering the process
intrinsically non-reciprocal. We thus identify a stationary geometric analog of the recently
proposed Asymmetric Dynamical Casimir Effect, in which rotation and frame-dragging
replace moving boundaries as the source of asymmetric mode mixing.
Our results unify classical superradiant scattering, quantum Bogoliubov amplification, and
asymmetric Casimir physics within a single horizonless geometry, demonstrating that
neither horizons nor time-dependent metrics are necessary for quantum particle creation
from the vacuum. The framework opens the door to future studies of higher-spin fields,
slowly varying rotation, and semiclassical backreaction effects.

At quantum scales, the classical description of spacetime no longer holds: the metric tensor develops intrinsic quantum fluctuations and cannot be treated as a smooth continuous field. Consequently, a black hole horizon also fails to remain an ideal smooth null hypersurface. Instead, it acquires quantum “wiggles,” corresponding to soft degrees of freedom—low-energy excitations capable of storing information as soft hair. These irregularities prevent the horizon from acting as a smooth two-dimensional surface at the Planck scale, giving it a highly jagged or fractal character. To model this deviation from smoothness, Barrow [Phys. Lett. B 808 (2020) 135643] proposed that the horizon is described by a fractal dimension, d=2+Δ , 0<Δ<1, with Δ quantifying the geometric deformation. For such a surface, the effective area scales as Aeff∝Rgd, instead of the classical A_{Cls}∝(R_g)^d. Based on the Bekenstein–Hawking argument that entropy counts horizon-covering Planck cells, this fractal surface increases the microscopic degrees of freedom, leading to the modified Barrow entropy S_B∝(A / A_{Pl})(1+Δ/2). Using the first law dM=T_BdS_B​, the corresponding temperature becomes a multiple of T_H. The heat capacity remains negative for all 0<Δ<1, so the thermodynamic instability of the Schwarzschild black hole persists. However, the reduced temperature suggests a slower evaporation process and the possible formation of a long-lived remnant. Geometrothermodynamics is reconstructed using this new fractalized entropy.

When excited states decay with energy $E_0-i\Gamma$, the time evolution operator $U(t)=e^{-iHt}$ does not obey $U^{\dagger}(t)U(t)=I$. Nonetheless, probability conservation is not lost if one includes both decay and excitation with energy $E_0+i\Gamma$, though it takes a different form. Specifically, if the eigenspectrum of a Hamiltonian is complete, then due to $CPT$ symmetry, a symmetry that holds for all physical systems, there must exist an operator $V$ that effects $VHV^{-1}=H^{\dagger}$, so that $V^{-1}U^{\dagger}(t)VU(t)=I$. As a consequence, because of probability conservation, the time delay associated with decay must be accompanied by an equal and opposite time advance for excitation. Thus, when a photon excites an atom, the spontaneous emission of a photon from the excited state must occur without any decay time delay at all. An effect of this form, together with an associated negative time delay, have recently been reported by Sinclair et al., PRX Quantum 3, 010314 (2022), and Angulo et al., arXiv:2409.03680 [quant-ph]. We show that the non-relativistic square well problem with a real potential possesses $PT$ symmetry in both the bound and scattering sectors, with complex conjugate pairs of energy eigenvalues in the scattering sector. In addition, we show that the square well scattering threshold branch point is an exceptional point (a characteristic of systems with an antilinear symmetry such as $PT$), a point at which the Hamiltonian becomes of non-diagonalizable, and thus manifestly non-Hermitian, Jordan-block form. The square well potential, one of the oldest known quantum-mechanical systems, provides an explicit realization of how antlinearity is more general than Hermiticity.

References:

Phys. Rev. D 112, L031903 (2025). (arXiv:2504.12068 [quant-ph]).

ArXiv: 2505.07798 {quant-ph].

Quantum biology is an emerging interdisciplinary field that investigates the fundamental quantum mechanisms underlying biological processes and their potential roles in the emergence and sustainability of life beyond Earth. While classical biochemistry successfully describes many aspects of life, experimental and theoretical evidence increasingly suggests that quantum effects such as coherence, tunneling, and entanglement play crucial roles in processes such as photosynthesis, enzyme catalysis, olfaction, and magnetoreception. In photosynthesis, energy transfer occurs through quantum coherence in pigment–protein complexes, while enzyme catalysis can involve proton or electron tunneling. Olfactory sensing may rely on electron tunneling, and magnetoreception in birds involves spin dynamics and entanglement in cryptochrome proteins. This work provides an in-depth analysis of these mechanisms, emphasizing how they might operate under cosmic conditions, including extreme temperatures, high-radiation, microgravity, and low-energy environments. Understanding these processes offers insights into the limits of quantum coherence in extreme environments, the potential emergence of life in diverse planetary and interstellar settings, and the fundamental principles governing complex systems. Additionally, potential applications in quantum-inspired technologies and biomimetic systems are discussed, highlighting how principles observed in living organisms can guide the design of novel quantum devices. By examining quantum mechanisms in both terrestrial and cosmic contexts, this work bridges physics, biology, and astrobiology, emphasizing the universal relevance of quantum principles to life across the cosmos.

Despite appealing theoretical features, higher time-derivative theories (HTDTs) are notoriously plagued by issues of instability—most prominently the emergence of ghost states, which signal the presence of unbounded-from-below Hamiltonians or non-normalisable states, that threaten the physical viability of these theories. Consequently, the construction of ghost-free representations is a central aim.

The Pais–Uhlenbeck (PU) model, a canonical example of a fourth-order differential system, is a paradigmatic example of an HTDT and encapsulates their essential challenges and features. Using its multi-Hamiltonian structures in conjunction with the Lie symmetries of the dynamical equation, one can construct distinct, but compatible, Poisson bracket formulations that preserve the system’s dynamics. Amongst other possibilities, this framework allows the recasting of models in a positive definite manner while leaving the dynamical flow unchanged, thus resolving the ghost problem. The application of the outlined approach has successfully demonstrated the construction of ghost-free representatives for the PU theory.

Introducing interactions to HTDTs generally challenges their stability further and poses a difficult problem. Going beyond the PU model, we here analyse an interacting extension of the system that admits closed-form solutions. This model suggests promising directions for the systematic construction of stable interacting HTDTs, future generalisations to field-theoretic settings, and further investigation into the quantisation of positive-definite PU models. A connection to an integrable realisation of the generalised Hénon–Heiles system (tied to Lax’s fifth-order KdV flow) is discussed.