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Linear response function

Index Linear response function

A linear response function describes the input-output relationship of a signal transducer such as a radio turning electromagnetic waves into music or a neuron turning synaptic input into a response. [1]

41 relations: Amplifier, Causality, Commutator, Convolution, Dispersion (optics), Electrical impedance, Electromagnetic radiation, Engineering, Fluctuation theorem, Force, Fourier transform, Fundamental solution, Green's function, Green–Kubo relations, Hamiltonian mechanics, Harmonic oscillator, Impulse response, Information theory, Interaction picture, Kramers–Kronig relations, Kubo formula, Leading-order term, Lindbladian, Magnetic susceptibility, Neuron, Ordinary differential equation, Particle statistics, Phase (waves), Physics, Propagator, Q factor, Resolvent formalism, Resonance, RLC circuit, Ryogo Kubo, Semilinear response, Signal transduction, Susceptibility, Synapse, Transfer function, Volterra series.

Amplifier

An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power of a signal (a time-varying voltage or current).

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Causality

Causality (also referred to as causation, or cause and effect) is what connects one process (the cause) with another process or state (the effect), where the first is partly responsible for the second, and the second is partly dependent on the first.

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Commutator

In mathematics, the commutator gives an indication of the extent to which a certain binary operation fails to be commutative.

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Convolution

In mathematics (and, in particular, functional analysis) convolution is a mathematical operation on two functions (f and g) to produce a third function, that is typically viewed as a modified version of one of the original functions, giving the integral of the pointwise multiplication of the two functions as a function of the amount that one of the original functions is translated.

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Dispersion (optics)

In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency.

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Electrical impedance

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied.

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Electromagnetic radiation

In physics, electromagnetic radiation (EM radiation or EMR) refers to the waves (or their quanta, photons) of the electromagnetic field, propagating (radiating) through space-time, carrying electromagnetic radiant energy.

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Engineering

Engineering is the creative application of science, mathematical methods, and empirical evidence to the innovation, design, construction, operation and maintenance of structures, machines, materials, devices, systems, processes, and organizations.

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Fluctuation theorem

The fluctuation theorem (FT), which originated from statistical mechanics, deals with the relative probability that the entropy of a system which is currently away from thermodynamic equilibrium (i.e., maximum entropy) will increase or decrease over a given amount of time.

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Force

In physics, a force is any interaction that, when unopposed, will change the motion of an object.

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Fourier transform

The Fourier transform (FT) decomposes a function of time (a signal) into the frequencies that make it up, in a way similar to how a musical chord can be expressed as the frequencies (or pitches) of its constituent notes.

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Fundamental solution

In mathematics, a fundamental solution for a linear partial differential operator is a formulation in the language of distribution theory of the older idea of a Green's function (although unlike Green's functions, fundamental solutions do not address boundary conditions).

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Green's function

In mathematics, a Green's function is the impulse response of an inhomogeneous linear differential equation defined on a domain, with specified initial conditions or boundary conditions.

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Green–Kubo relations

The Green–Kubo relations (Melville S. Green 1954, Ryogo Kubo 1957) give the exact mathematical expression for transport coefficients \gamma in terms of integrals of time correlation functions.

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Hamiltonian mechanics

Hamiltonian mechanics is a theory developed as a reformulation of classical mechanics and predicts the same outcomes as non-Hamiltonian classical mechanics.

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Harmonic oscillator

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, F, proportional to the displacement, x: where k is a positive constant.

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Impulse response

In signal processing, the impulse response, or impulse response function (IRF), of a dynamic system is its output when presented with a brief input signal, called an impulse.

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Information theory

Information theory studies the quantification, storage, and communication of information.

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Interaction picture

In quantum mechanics, the interaction picture (also known as the Dirac picture after Paul Dirac) is an intermediate representation between the Schrödinger picture and the Heisenberg picture.

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Kramers–Kronig relations

The Kramers–Kronig relations are bidirectional mathematical relations, connecting the real and imaginary parts of any complex function that is analytic in the upper half-plane.

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Kubo formula

The Kubo formula is an equation which expresses the linear response of an observable quantity due to a time-dependent perturbation.

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Leading-order term

The leading-order terms (or corrections) within a mathematical equation, expression or model are the terms with the largest order of magnitude.

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Lindbladian

In quantum mechanics, the Gorini–Kossakowski–Sudarshan–Lindblad equation (GKSL equation, named after Vittorio Gorini, Andrzej Kossakowski, George Sudarshan and Göran Lindblad), master equation in Lindblad form, or Lindbladian is the most general type of Markovian and time-homogeneous master equation describing (in general non-unitary) evolution of the density matrix that preserves the laws of quantum mechanics (i.e., is trace-preserving and completely positive for any initial condition).

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Magnetic susceptibility

In electromagnetism, the magnetic susceptibility (Latin: susceptibilis, "receptive"; denoted) is one measure of the magnetic properties of a material.

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Neuron

A neuron, also known as a neurone (British spelling) and nerve cell, is an electrically excitable cell that receives, processes, and transmits information through electrical and chemical signals.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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Particle statistics

Particle statistics is a particular description of multiple particles in statistical mechanics.

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Phase (waves)

Phase is the position of a point in time (an instant) on a waveform cycle.

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Physics

Physics (from knowledge of nature, from φύσις phýsis "nature") is the natural science that studies matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion and behavior through space and time and that studies the related entities of energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines and, through its inclusion of astronomy, perhaps the oldest. Over the last two millennia, physics, chemistry, biology, and certain branches of mathematics were a part of natural philosophy, but during the scientific revolution in the 17th century, these natural sciences emerged as unique research endeavors in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms studied by other sciences and suggest new avenues of research in academic disciplines such as mathematics and philosophy. Advances in physics often enable advances in new technologies. For example, advances in the understanding of electromagnetism and nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization; and advances in mechanics inspired the development of calculus.

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Propagator

In 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 time, or to travel with a certain energy and momentum.

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Q factor

In physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how underdamped an oscillator or resonator is, and characterizes a resonator's bandwidth relative to its centre frequency.

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Resolvent formalism

In mathematics, the resolvent formalism is a technique for applying concepts from complex analysis to the study of the spectrum of operators on Banach spaces and more general spaces.

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Resonance

In physics, resonance is a phenomenon in which a vibrating system or external force drives another system to oscillate with greater amplitude at specific frequencies.

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RLC circuit

An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel.

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Ryogo Kubo

was a Japanese mathematical physicist, best known for his works in statistical physics and non-equilibrium statistical mechanics.

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Semilinear response

Semi-linear response theory (SLRT) is an extension of linear response theory (LRT) for mesoscopic circumstances: LRT applies if the driven transitions are much weaker/slower than the environmental relaxation/dephasing effect, while SLRT assumes the opposite conditions.

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Signal transduction

Signal transduction is the process by which a chemical or physical signal is transmitted through a cell as a series of molecular events, most commonly protein phosphorylation catalyzed by protein kinases, which ultimately results in a cellular response.

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Susceptibility

Susceptibility may refer to.

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Synapse

In the nervous system, a synapse is a structure that permits a neuron (or nerve cell) to pass an electrical or chemical signal to another neuron or to the target efferent cell.

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Transfer function

In engineering, a transfer function (also known as system function or network function) of an electronic or control system component is a mathematical function giving the corresponding output value for each possible value of the input to the device.

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Volterra series

The Volterra series is a model for non-linear behavior similar to the Taylor series.

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Redirects here:

Linear response, Linear response theory.

References

[1] https://en.wikipedia.org/wiki/Linear_response_function

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