Related Experiment Video
Updated: Mar 21, 2026
11:21
Cooling an Optically Trapped Ultracold Fermi Gas by Periodical Driving
Published on: March 30, 2017
8.0K
Lyapunov decay in quantum irreversibility.
Ignacio García-Mata1, Augusto J Roncaglia2, Diego A Wisniacki2
1Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET-UNMdP, Mar del Plata, Argentina Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Buenos Aires, Argentina nacho.garcia.mata@gmail.com.
Summary
The Loschmidt echo, a measure of quantum system stability, reveals universal behavior in chaotic systems. Averaging fidelity over the Haar measure recovers the Lyapunov exponent, independent of initial states.
Area of Science:
- Quantum mechanics
- Statistical physics
- Chaos theory
Background:
- The Loschmidt echo (fidelity) quantifies irreversibility in quantum systems under perturbations.
- Different dynamical regimes are observed based on time and perturbation strength.
- For chaotic systems, a perturbation-independent decay regime exists, linked to the Lyapunov exponent.
Purpose of the Study:
- To introduce a quantity analogous to fidelity for infinite-dimensional systems.
- To demonstrate the universality of the Lyapunov regime in such systems.
- To investigate the quantum stadium billiard as a model system.
Main Methods:
- Defining an analogous quantity for infinite-dimensional Hilbert spaces.
- Analyzing the quantum stadium billiard.
- Averaging fidelity over the Haar measure to remove state dependence.
Main Results:
- The Lyapunov decay regime is shown to be universally observable.
- The introduced quantity facilitates the study of quantum chaos in infinite dimensions.
- The quantum stadium billiard exhibits the predicted universal behavior.
Conclusions:
- The universality of the Lyapunov regime is confirmed for infinite-dimensional quantum systems.
- The study provides a method to observe quantum chaos indicators independent of initial state preparation.
- This work extends the understanding of quantum irreversibility and chaos.
Related Concept Videos
01:10Entropy Change in Reversible Processes
3.4K
In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
3.4K
01:14Reversible and Irreversible Processes
6.1K
The thermodynamic processes can be classified into reversible and irreversible processes. The processes that can be restored to their initial state are called reversible processes. It is only possible if the process is in quasi-static equilibrium, i.e., it takes place in infinitesimally small steps, and the system remains at equilibrium However, these are ideal processes and do not occur naturally. An ideal system undergoing a reversible process is always in thermodynamic equilibrium within...
6.1K
01:22Limits of the First Law of Thermodynamics
97
Spontaneous processes, like a rock falling to the ground or sodium reacting with chlorine, occur without external work and often involve a decrease in the system‘s energy. However, certain endothermic processes, such as the dissolution of sodium chloride in water, occur spontaneously even though they increase the energy of the system. This limitation suggests that the First Law of Thermodynamics, which states that the total energy of a system is constant in an isolated system, cannot...
97
01:30Current Growth And Decay In RL Circuits
4.9K
The current growth and decay in RL circuits can be understood by considering a series RL circuit consisting of a resistor, an inductor, a constant source of emf, and two switches. When the first switch is closed, the circuit is equivalent to a single-loop circuit consisting of a resistor and an inductor connected to a source of emf. In this case, the source of emf produces a current in the circuit. If there were no self-inductance in the circuit, the current would rise immediately to a steady...
4.9K
01:14The Entropy as a State Function
68
Consider an arbitrary process that moves between two specific states (A and B) in a cyclic manner. This process is reversible and broken down into smaller parts that each follow a Carnot cycle. A Carnot cycle has two isothermal (constant temperature) processes. During these processes, the ratio of the amount of heat transferred to their respective temperature remains constant. The other two processes in the Carnot cycle are also reversible but adiabatic, which means they occur without any heat...
68
01:29Improper Integrals: Infinite Intervals
192
An integral is classified as improper due to an infinite interval when at least one of its limits of integration extends to positive or negative infinity. In such cases, the region under the curve is unbounded, and standard techniques for evaluating definite integrals are not directly applicable. Instead, the improper integral is defined through a limiting process that allows one to determine whether the accumulated area remains finite despite the infinite domain.Application to Exponential...
192