Tracking Adiabaticity in Non-Equilibrium Many-Body Systems: The Hard Case of the X-ray Photoemission in Metals

Abstract

The level of adiabaticity determines many properties of time-dependent quantum systems. However, a reliable and easy-to-apply criterion to check and track it remains an open question, especially for complex many-body systems. Here we test techniques based on metrics which have been recently proposed to quantitatively characterize and track adiabaticity. We investigate the time evolution of x-ray photoemission in metals, which displays a strongly out-of-equilibrium character, continuum energy spectrum, and experiences the Anderson orthogonality catastrophe: a nightmarish scenario for this type of test. Our results show that the metrics-based methods remains valid. In particular, we demonstrate that the natural local density distance is able not only to track adiabaticity, but also to provide information not captured by the corresponding Bures' or trace distances about the system's dynamics. In the process, we establish an explicit upper limit for this local density distance in terms of the trace distance, and derive a simple analytical solution that accurately describes the time evolution of a Fermi gas with a localized scattering potential for a large range of parameters. We also demonstrate that, for x-ray photoemission, the quantum adiabatic criterion, as commonly used, fails to predict and track adiabaticity. The local particle density is typically much simpler to compute than the corresponding quantum state and it is experimentally measurable: this makes the method tested extremely appealing.

References in corpus (40)

• Adiabatic Quantum Computing
• The numerical renormalization group method for quantum impurity systems
• Quantum many-body systems out of equilibrium
• Shortcuts to adiabaticity: concepts, methods, and applications
• Bounds for the adiabatic approximation with applications to quantum computation
• Generalized Geometric Quantum Speed Limits
• Experimental realization of stimulated Raman shortcut-to-adiabatic passage with cold atoms
• Quantum Thermodynamic Cycles and Quantum Heat Engines (II)
• Adiabatic Theorem without a Gap Condition
• Inconsistency in the application of the adiabatic theorem
• Consistency of the Adiabatic Theorem
• Universal Work Fluctuations during Shortcuts To Adiabaticity by Counterdiabatic Driving
• Quantitative conditions do not guarantee the validity of the adiabatic approximation
• Sufficiency Criterion for the Validity of the Adiabatic Approximation
• Adiabatic dynamics in open quantum critical many-body systems
• Adiabaticity in open quantum systems
• A Quantum Approach to Classical Statistical Mechanics
• Thermodynamic length for far from equilibrium quantum systems
• Environment-invariant measure of distance between evolutions of an open quantum system
• Measuring the photoelectron emission delay in the molecular frame
• Fermi gas response to time-dependent perturbations
• Quantum mechanics in metric space: wave functions and their densities
• Work-distribution quantumness and irreversibility when crossing a quantum phase transition in finite time
• Quantum adiabatic theorem in light of the Marzlin-Sanders inconsistency
• The heat and work of quantum thermodynamic processes with quantum coherence
• Adiabatic theorem for closed quantum systems initialized at finite temperature
• Many-body effects on the thermodynamics of closed quantum systems
• Necessary and sufficient condition for quantum adiabaticity in a driven one-dimensional impurity-fluid system
• Metric-space approach for distinguishing quantum phase transitions in spin-imbalanced systems
• Metric space approach to potentials and its relevance to density functional theory
• Metric space analysis of systems immersed in a magnetic field
• Quantum adiabatic cycles and their breakdown
• Measuring adiabaticity in non-equilibrium quantum systems
• Fermionic correlations as metric distances: a useful tool for materials science
• Characterizing Adiabaticity in Quantum Many-Body Systems at Finite Temperature
• How to experimentally evaluate the adiabatic condition for quantum annealing
• Metrics for two electron random potential systems
• Fidelity-based distance bounds for $N$-qubit approximate quantum error correction
• Analytical Diagonalization of Fermi Gas-like Hamiltonians using the Sommerfeld-Watson Transformation
• Transport in Single Quantum Dots: A Review from Linear Response to Nonlinear Regimes

Cited by in corpus (1)

• Sticking coefficient for atoms impinging on a metallic surfaces, and the x-ray photoemission by metals