Search results for "Uncertainty principle"
showing 10 items of 10 documents
Quantum like modelling of decision making: quantifying uncertainty with the aid of the Heisenberg-Robertson inequality
2018
This paper contributes to quantum-like modeling of decision making (DM) under uncertainty through application of Heisenberg’s uncertainty principle (in the form of the Robertson inequality). In this paper we apply this instrument to quantify uncertainty in DM performed by quantum-like agents. As an example, we apply the Heisenberg uncertainty principle to the determination of mutual interrelation of uncertainties for “incompatible questions” used to be asked in political opinion pools. We also consider the problem of representation of decision problems, e.g., in the form of questions, by Hermitian operators, commuting and noncommuting, corresponding to compatible and incompatible questions …
Heisenberg Uncertainty Relation in Quantum Liouville Equation
2009
We consider the quantum Liouville equation and give a characterization of the solutions which satisfy the Heisenberg uncertainty relation. We analyze three cases. Initially we consider a particular solution of the quantum Liouville equation: the Wigner transformf(x,v,t) of a generic solutionψ(x;t) of the Schrödinger equation. We give a representation ofψ(x,t) by the Hermite functions. We show that the values of the variances ofxandvcalculated by using the Wigner functionf(x,v,t) coincide, respectively, with the variances of position operatorX^and conjugate momentum operatorP^obtained using the wave functionψ(x,t). Then we consider the Fourier transform of the density matrixρ(z,y,t) =ψ∗(z,t)…
Evolution of a Quantum System: Lifetime of a Determinant
1976
A measure of the ''dependency'' of a many-particle system is defined and its time dependence is evaluated for systems initially described by a single Slater determinant. An uncertainty product between the energy spread of the initial determinant and the lifetime of a system's independence is established. Numerical estimates of some lifetimes are given. They are not so long as to be reassuring for nuclear time-dependent Hartree--Fock calculations. Each separate case ought to be checked. 1 table.
Annihilating sets for the short time Fourier transform
2010
Abstract We obtain a class of subsets of R 2 d such that the support of the short time Fourier transform (STFT) of a signal f ∈ L 2 ( R d ) with respect to a window g ∈ L 2 ( R d ) cannot belong to this class unless f or g is identically zero. Moreover we prove that the L 2 -norm of the STFT is essentially concentrated in the complement of such a set. A generalization to other Hilbert spaces of functions or distributions is also provided. To this aim we obtain some results on compactness of localization operators acting on weighted modulation Hilbert spaces.
Revealing Hidden Quantum Correlations in an Electromechanical Measurement.
2018
Under a strong quantum measurement, the motion of an oscillator is disturbed by the measurement back-action, as required by the Heisenberg uncertainty principle. When a mechanical oscillator is continuously monitored via an electromagnetic cavity, as in a cavity optomechanical measurement, the back-action is manifest by the shot noise of incoming photons that becomes imprinted onto the motion of the oscillator. Following the photons leaving the cavity, the correlations appear as squeezing of quantum noise in the emitted field. Here we observe such "ponderomotive" squeezing in the microwave domain using an electromechanical device made out of a superconducting resonator and a drumhead mechan…
Foundations of quantum mechanics and their impact on contemporary society
2018
Nearing a century since its inception, quantum mechanics is as lively as ever. Its signature manifestations, such as superposition, wave-particle duality, uncertainty principle, entanglement and nonlocality, were long confronted as weird predictions of an incomplete theory, paradoxes only suitable for philosophical discussions, or mere mathematical artifacts with no counterpart in the physical reality. Nevertheless, decades of progress in the experimental verification and control of quantum systems have routinely proven detractors wrong. While fundamental questions still remain wide open on the foundations and interpretations of quantum mechanics, its modern technological applications have …
Duality-invariant Einstein-Planck relation and the speed of light at very short wavelengths
2011
We propose a generalized Einstein-Planck relation for photons which is invariant under the change $\ensuremath{\lambda}/a{l}_{P}$ to $a{l}_{P}/\ensuremath{\lambda}$, $\ensuremath{\lambda}$ being the photon wavelength, ${l}_{P}$ Planck's length, and $a$ a numerical constant. This yields a wavelength-dependent speed of light $v(\ensuremath{\lambda})=c/(1+{a}^{2}({l}_{P}/\ensuremath{\lambda}{)}^{2})$, with $c$ the usual speed of light in vacuo, indicating that the speed of light should decrease for sufficiently short wavelengths. We discuss the conceptual differences with the previous proposals related to a possible decrease of the speed of light for very short wavelengths based on quantum flu…
Squeezing induced by spontaneous rotational symmetry breaking
2009
In this communication we study in depth the phenomenon of quadrature squeezing generated via spontaneous rotational symmetry breaking discussed for the first time in [1]. The idea can be put in short as follows. Consider a degenerate optical parametric oscillator (DOPO) tuned to the first family of transverse modes at the signal frequency, and having perfectly spherical mirrors. When pumped above threshold with a Gaussian beam and within a classical description, it is easy to show that a TEM 10 mode with an arbitrary orientation (measured by θ at Fig. 1) emerges at the subharmonic, hence breaking the rotational symmetry of the system in the transverse plane. Quantum effects are then quite i…
Hyper-Entanglement in Time and Frequency
2019
Hyper-entanglement, i.e. entanglement in more than one degree of freedom, enables a multiplicative increase in Hilbert space size. Such systems can be treated as multi-partite even though the number of state particles is not increased, making them highly attractive for applications in high-capacity quantum communications and information processing [1]. Until now, such states have been realized only using combinations of fully independent degrees of freedom, described by commuting operators, such as polarization and optical paths. Time and frequency, in turn, are linked and described by non-commuting operators. Here, using two discrete forms of energy-time entanglement we demonstrate that ti…
Electron structure, ultra-dense hydrogen and low energy nuclear reactions
2019
In this paper, a simple Zitterbewegung electron model, proposed in a previous work, is presented from a different perspective based on the principle of mass- frequency equivalence. A geometric- electromagnetic interpretation of mass, relativistic mass, De Broglie wavelength, Proca, Klein- Gordon, Dirac and Aharonov- Bohm equations in agreement with the model is proposed. A non-relativistic, Zitterbewegung interpretation of the 3.7 keV deep hydrogen level found by J. Naudts is presented. According to this perspective, ultra-dense hydrogen can be conceived as a coherent chain of bosonic electrons with protons or deuterons located in the center of their Zitterbewegung orbits. This approach sug…