Flattening the Curve with Einstein's Quantum Elevator: Hermitization of Non-Hermitian Hamiltonians via a Generalized Vielbein Formalism

Abstract

The formalism for non-Hermitian quantum systems sometimes blurs the underlying physics. We present a systematic study of the vielbein-like formalism which transforms the Hilbert space bundles of non-Hermitian systems into the conventional ones, rendering the induced Hamiltonian to be Hermitian. In other words, any non-Hermitian Hamiltonian can be "transformed" into a Hermitian one without altering the physics. Thus we show how to find a reference frame (corresponding to Einstein's quantum elevator) in which a non-Hermitian system, equipped with a non-trivial Hilbert space metric, reduces to a Hermitian system within the standard formalism of quantum mechanics.

arXiv comment10 pages, 2 figures

References in corpus (33)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Making Sense of Non-Hermitian Hamiltonians
• Complex Extension of Quantum Mechanics
• Non-Hermitian Physics
• Pseudo-Hermitian Representation of Quantum Mechanics
• Superspace Duality in Low-Energy Superstrings
• Two-Vierbein Formalism for String-Inspired Axionic Gravity
• Biorthogonal Quantum Mechanics
• Exceptional Points of Non-hermitian Operators
• Quantum exceptional points of non-Hermitian Hamiltonians and Liouvillians: The effects of quantum jumps
• Pseudo-Hermiticity and Generalized PT- and CPT-Symmetries
• Resolution of Gauge Ambiguities in Ultrastrong-Coupling Cavity QED
• Local PT symmetry violates the no-signaling principle
• Universality classes of non-Hermitian random matrices
• Non-Hermitian Hamiltonians and no-go theorems in quantum information
• Time-dependent version of cryptohermitian quantum theory
• Operator (quasi-)similarity, quasi-Hermitian operators and all that
• Increase of entanglement by local PT -symmetric operations
• The C Operator in PT-Symmetric Quantum Theories
• Consistency of PT-symmetric quantum mechanics
• Hunting for the non-Hermitian exceptional points with fidelity susceptibility
• Gauge invariance of the Dicke and Hopfield models
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Gauge freedom, quantum measurements, and time-dependent interactions in cavity and circuit QED
• Gauge Principle and Gauge Invariance in Two-Level Systems
• Gauge Principle and Gauge Invariance in Quantum Two-Level Systems
• Time-Dependent Hilbert Spaces, Geometric Phases, and General Covariance in Quantum Mechanics
• T-duality off shell in 3D Type II superspace
• Density Matrix Formalism for PT-Symmetric Non-Hermitian Hamiltonians with the Lindblad Equation
• Gauging Unbroken Symmetries in F-theory
• Is PT-symmetric quantum theory false as a fundamental theory?
• Violation of Invariance of Entanglement Under Local PT Symmetric Unitary
• Equivalent Relations between Quantum Dynamics as Derived from a Gauge Transformation

Cited by in corpus (37)

• Two-dimensional non-Hermitian skin effect in an ultracold Fermi gas
• Dynamically crossing diabolic points while encircling exceptional curves: A programmable symmetric-asymmetric multimode switch
• Non-Hermitian Stark Many-Body Localization
• Non-Markovian Quantum Exceptional Points
• Restoring Adiabatic State Transfer in Time-Modulated Non-Hermitian Systems
• Activating non-Hermitian skin modes by parity-time symmetry breaking
• Experimental Liouvillian exceptional points in a quantum system without Hamiltonian singularities
• Entanglement Dynamics in Anti-$\mathcal{P}\mathcal{T}$-Symmetric Systems
• Emergent parallel transport and curvature in Hermitian and non-Hermitian quantum mechanics
• Quantum Liouvillian exceptional and diabolical points for bosonic fields with quadratic Hamiltonians: The Heisenberg-Langevin equation approach
• Extension of Noether's theorem in PT-symmetric systems and its experimental demonstration in an optical setup
• Composite quantum Coriolis forces
• Hybrid form of quantum theory with non-Hermitian Hamiltonians
• Liouvillian and Hamiltonian exceptional points of atomic vapors: The spectral signatures of quantum jumps
• Entanglement Hamiltonian and effective temperature of non-Hermitian quantum spin ladders
• Quasi-Hermitian formulation of quantum mechanics using two conjugate Schrödinger equations
• Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions
• Non-Hermitian Generalization of Rayleigh-Schrödinger Perturbation Theory
• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
• Non-stationary non-Hermitian "wrong-sign'' quantum oscillators and their meaningful physical interpretation
• Heisenberg and Heisenberg-Like Representations via Hilbert Space Bundle Geometry in the Non-Hermitian Regime
• Achieving the Quantum Fisher Information Bound in Pseudo-Hermitian Sensors
• Entanglement between uncoupled modes with time-dependent complex frequencies
• Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space
• Non-stationary quantum mechanics in hybrid non-Hermitian interaction representation
• Topological state permutations in time-modulated non-Hermitian multiqubit systems with suppressed non-adiabatic transitions
• Intrinsic exceptional point -- a challenge in quantum theory
• Few-grid-point simulations of Big Bang singularity in quantum cosmology
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables
• Necessary condition for information transfer under simulated parity-time-symmetric evolution
• Decomposition of a system in pseudo-Hermitian quantum mechanics
• Covariant formulation of the Berry connection in non-Hermitian systems
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Emergence and localization of exceptional points in an exactly solvable toy model
• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model
• Reconstruction of full-space quantum Hamiltonian from its effective, energy-dependent model-space projection
• Twin Hamiltonians, three types of the Dyson maps, and the probabilistic interpretation problem in quasi-Hermitian quantum mechanics