PropagatorIn quantum mechanics and quantum field theory, the propagator is a function that specifies the probability amplitude for a particle to travel from one place to another in a given period of time, or to travel with a certain energy and momentum. In Feynman diagrams, which serve to calculate the rate of collisions in quantum field theory, virtual particles contribute their propagator to the rate of the scattering event described by the respective diagram.
Path integral formulationThe path integral formulation is a description in quantum mechanics that generalizes the action principle of classical mechanics. It replaces the classical notion of a single, unique classical trajectory for a system with a sum, or functional integral, over an infinity of quantum-mechanically possible trajectories to compute a quantum amplitude. This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical quantization.
Quantum thermodynamicsQuantum thermodynamics is the study of the relations between two independent physical theories: thermodynamics and quantum mechanics. The two independent theories address the physical phenomena of light and matter. In 1905, Albert Einstein argued that the requirement of consistency between thermodynamics and electromagnetism leads to the conclusion that light is quantized obtaining the relation . This paper is the dawn of quantum theory. In a few decades quantum theory became established with an independent set of rules.
Quantum heat engines and refrigeratorsA quantum heat engine is a device that generates power from the heat flow between hot and cold reservoirs. The operation mechanism of the engine can be described by the laws of quantum mechanics. The first realization of a quantum heat engine was pointed out by Scovil and Schulz-DuBois in 1959, showing the connection of efficiency of the Carnot engine and the 3-level maser. Quantum refrigerators share the structure of quantum heat engines with the purpose of pumping heat from a cold to a hot bath consuming power first suggested by Geusic, Schulz-DuBois, De Grasse and Scovil.
ThermodynamicsThermodynamics is a branch of physics that deals with heat, work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed by the four laws of thermodynamics which convey a quantitative description using measurable macroscopic physical quantities, but may be explained in terms of microscopic constituents by statistical mechanics.
Second law of thermodynamicsThe second law of thermodynamics is a physical law based on universal experience concerning heat and energy interconversions. One simple statement of the law is that heat always moves from hotter objects to colder objects (or "downhill"), unless energy in some form is supplied to reverse the direction of heat flow. Another definition is: "Not all heat energy can be converted into work in a cyclic process." The second law of thermodynamics in other versions establishes the concept of entropy as a physical property of a thermodynamic system.
Third law of thermodynamicsThe third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field. At absolute zero (zero kelvins) the system must be in a state with the minimum possible energy. Entropy is related to the number of accessible microstates, and there is typically one unique state (called the ground state) with minimum energy.
Timeline of thermodynamicsA timeline of events in the history of thermodynamics. 1650 – Otto von Guericke builds the first vacuum pump 1660 – Robert Boyle experimentally discovers Boyle's Law, relating the pressure and volume of a gas (published 1662) 1665 – Robert Hooke published his book Micrographia, which contained the statement: "Heat being nothing else but a very brisk and vehement agitation of the parts of a body." 1667 – J. J. Becher puts forward a theory of combustion involving combustible earth in his book Physica subterranea (see Phlogiston theory).
Quantum mechanicsQuantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales.
Partition function (quantum field theory)In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time versions of statistical mechanics partition functions, giving rise to a close connection between these two areas of physics. Partition functions can rarely be solved for exactly, although free theories do admit such solutions. Instead, a perturbative approach is usually implemented, this being equivalent to summing over Feynman diagrams.
Feynman diagramIn theoretical physics, a Feynman diagram is a pictorial representation of the mathematical expressions describing the behavior and interaction of subatomic particles. The scheme is named after American physicist Richard Feynman, who introduced the diagrams in 1948. The interaction of subatomic particles can be complex and difficult to understand; Feynman diagrams give a simple visualization of what would otherwise be an arcane and abstract formula.
Schwinger's quantum action principleThe Schwinger's quantum action principle is a variational approach to quantum mechanics and quantum field theory. This theory was introduced by Julian Schwinger in a series of articles starting 1950. In Schwingers approach, the action principle is targeted towards quantum mechanics. The action becomes a quantum action, i.e. an operator, . Although it is superficially different from the path integral formulation where the action is a classical function, the modern formulation of the two formalisms are identical.
Free particleIn physics, a free particle is a particle that, in some sense, is not bound by an external force, or equivalently not in a region where its potential energy varies. In classical physics, this means the particle is present in a "field-free" space. In quantum mechanics, it means the particle is in a region of uniform potential, usually set to zero in the region of interest since the potential can be arbitrarily set to zero at any point in space. The classical free particle is characterized by a fixed velocity v.
Quantum field theoryIn theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles. QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles.
Quantum electrodynamicsIn particle physics, quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved. QED mathematically describes all phenomena involving electrically charged particles interacting by means of exchange of photons and represents the quantum counterpart of classical electromagnetism giving a complete account of matter and light interaction.
École Polytechnique Fédérale de LausanneThe École polytechnique fédérale de Lausanne (EPFL; English: Swiss Federal Institute of Technology in Lausanne; Eidgenössische Technische Hochschule Lausanne) is a public research university in Lausanne, Switzerland. Established in 1853, EPFL has placed itself as a university specializing in engineering and natural sciences. EPFL is part of the ETH Domain, which is directly dependent on the Federal Department of Economic Affairs, Education and Research.
Particle in a boxIn quantum mechanics, the particle in a box model (also known as the infinite potential well or the infinite square well) describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another.
Classical economicsClassical economics, classical political economy, or Smithian economics is a school of thought in political economy that flourished, primarily in Britain, in the late 18th and early-to-mid 19th century. Its main thinkers are held to be Adam Smith, Jean-Baptiste Say, David Ricardo, Thomas Robert Malthus, and John Stuart Mill. These economists produced a theory of market economies as largely self-regulating systems, governed by natural laws of production and exchange (famously captured by Adam Smith's metaphor of the invisible hand).
Classical liberalismClassical liberalism is a political tradition and a branch of liberalism that advocates free market and laissez-faire economics; and civil liberties under the rule of law, with special emphasis on individual autonomy, limited government, economic freedom, political freedom and freedom of speech. Classical liberalism, contrary to liberal branches like social liberalism, looks more negatively on social policies, taxation and the state involvement in the lives of individuals, and it advocates deregulation.
Interpretations of quantum mechanicsAn interpretation of quantum mechanics is an attempt to explain how the mathematical theory of quantum mechanics might correspond to experienced reality. Although quantum mechanics has held up to rigorous and extremely precise tests in an extraordinarily broad range of experiments, there exist a number of contending schools of thought over their interpretation. These views on interpretation differ on such fundamental questions as whether quantum mechanics is deterministic or stochastic, local or non-local, which elements of quantum mechanics can be considered real, and what the nature of measurement is, among other matters.
