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Phase Transitions

Phase Transitions

A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...

Phase Transitions

Phase Transitions

Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...

Phase Diagram

Phase Diagram

The phase of a given substance depends on the pressure and temperature. Thus, plots of pressure versus temperature showing the phase in each region provide considerable insights into the thermal properties of substances. Such plots are known as phase diagrams. For instance, in the phase diagram for water (Figure 1), the solid curve boundaries between the phases indicate phase transitions (i.e., temperatures and pressures at which the phases coexist).

Phase Diagram

Phase Diagram

A phase diagram is a graphical representation of the physical states of a substance under different conditions of temperature and pressure. It shows the boundaries between solid, liquid, and gas phases and the conditions at which these phases coexist in equilibrium. An area in a phase diagram represents a single phase, whereas lines or phase boundaries represent the equilibrium between two phases.In the phase diagram of water, the boundary line between the solid and liquid states illustrates...

The Phase Rule

The Phase Rule

The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...

Entropy Changes Accompanying Specific Processes

Entropy Changes Accompanying Specific Processes

Entropy, a measure of disorder in a system, changes during phase transitions like freezing or boiling. At the transition temperature Ttrs, where two phases are in equilibrium, the phase transition is a reversible process. The entropy change can be calculated from a substance's enthalpy of transition using the equation ΔStrs = ΔtrsH /Ttrs.When a perfect gas expands isothermally from one volume to another, entropy increases logarithmically with volume. Conversely, isothermal compression results...

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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform

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Geometric phases and quantum phase transitions in open systems.

Alexander I Nesterov¹, S G Ovchinnikov

¹Departamento de Física, CUCEI, Universidad de Guadalajara, Av. Revolución 1500, Guadalajara, Codigo Postal 44420, Jalisco, México. nesterov@cencar.udg.mx

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|September 4, 2008

Summary

This study links quantum phase transitions to geometric phases in open quantum systems. The first-order quantum phase transition in a dissipative Ising model is characterized by its geometric phase.

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Area of Science:

Quantum mechanics
Condensed matter physics
Non-Hermitian systems

Background:

Open quantum systems exhibit complex dynamics influenced by dissipation.
Non-Hermitian Hamiltonians are crucial for describing systems with gain or loss.
Quantum phase transitions (QPTs) signify abrupt changes in a system's ground state properties.

Purpose of the Study:

To establish a relationship between quantum phase transitions and complex geometric phases in open quantum systems.
To investigate the geometric phase of the ground state in a specific dissipative model.
To characterize the order of the quantum phase transition in the studied system.

Main Methods:

Governing open quantum systems with a non-Hermitian effective Hamiltonian.
Analyzing systems with accidental crossings of eigenvalues.
Evaluating the geometric phase associated with the ground state.
Utilizing the one-dimensional dissipative Ising model in a transverse magnetic field.

Main Results:

A direct relationship is established between QPTs and complex geometric phases.
The geometric phase for the ground state of the 1D dissipative Ising model is calculated.
The quantum phase transition in this model is identified as a first-order transition.

Conclusions:

Geometric phases offer a new perspective for understanding QPTs in open, non-Hermitian systems.
The first-order nature of the QPT in the dissipative Ising model is confirmed through geometric phase analysis.
This work provides a framework for exploring QPTs in dissipative quantum technologies.