Related papers: No-Existence Of Generalize Diffusion
We consider the standard two-party communication model. The central problem studied in this article is how much one can save in information complexity by allowing an error of $\epsilon$. For arbitrary functions, we obtain lower bounds and…
In this paper we propose the use of $\phi$-divergences as test statistics to verify simple hypotheses about a one-dimensional parametric diffusion process $\de X_t = b(X_t, \theta)\de t + \sigma(X_t, \theta)\de W_t$, from discrete…
In the framework of quantum field theory (QFT) on noncommutative (NC) space-time with the symmetry group $O(1,1)\times SO(2)$, we prove that the Jost-Lehmann-Dyson representation, based on the causality condition taken in connection with…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
In this paper, we reconsider the communication model used in the no-go theorems on the impossibility of quantum bit commitment and oblivious transfer. We state that a macroscopic classical channel may not be replaced with a quantum channel…
It is demonstrated that a nonrelativistic quantum scale anomaly manifests itself in the appearance of composite operators with complex scaling dimensions. In particular, we study nonrelativistic quantum mechanics with an inverse square…
A description in terms of transition rates among cells is used to analyze self-diffusion of hard spheres in the fluid phase. Cell size is assumed much larger than the mean free path. Transition state theory is used to obtain an equation…
The phase conjugation of an unknown Gaussian state cannot be realized perfectly by any physical process. A semi-classical argument is used to derive a tight lower bound on the noise that must be introduced by an approximate phase…
We prove that there is no algorithm that can determine whether or not a finitely presented group has a non-trivial finite quotient; indeed, this remains undecidable among the fundamental groups of compact, non-positively curved square…
A Bethe-Salpeter treatment of Cooper pairs (CPs) based on an ideal Fermi gas (IFG) "sea"' yields the familiar negative-energy, two-particle bound-state if two-hole CPs are ignored, but is meaningless otherwise as it gives purely-imaginary…
In the resource theory of non-stabilizerness, we prove that stabilizer operations cannot replicate or broadcast the "magic" resource of all quantum states in an arbitrary finite dimension. Moreover, we show that even in unrestricted…
We consider the Maxwell-Higgs system in the broken phase, described in terms of a Kalb-Ramond field interacting with the electromagnetic field through a topological coupling. We then study the creation operators of states which respectively…
It is well known that quantum-mechanical perturbation theory often give rise to divergent series that require proper resummation. Here I discuss simple ways in which these divergences can be avoided in the first place. Using the elementary…
Asymptotic expansion of the second-order linear ordinary differential equation Psi'' + k^2 f(z) Psi = 0, in which the real constant k is large and f = O(1), can be carried out in the manner of Liouville and Green provided f does not vanish.…
We will examine a particular mathematical derivation in a paper by P. Falkensteiner and H. Grosse (F&G) [1]. In [1] a quantity "delta(A)" is defined. This quantity is generated when the normal ordered generalized charge operator undergoes a…
For states in infinite dimensional Hilbert spaces entanglement quantities like the entanglement of distillation can become infinite. This leads naturally to the question, whether one system in such an infinitely entangled state can serve as…
We answer a question that was asked by Albert Baernstein II, regarding the coefficients of circular symmetrization. The conjecture is not true generically.
We show that the value of a general two-prover quantum game cannot be computed by a semi-definite program ofvpolynomial size (unless P=NP), a method that has been successful in more restricted quantum games. More precisely, we show that…
Density operators are one of the key ingredients of quantum theory. They can be constructed in two ways: via a convex sum of 'doubled kets' (i.e. mixing), and by tracing out part of a 'doubled' two-system ket (i.e. dilation). Both…
The author studies the diffusion problem $u_t=u_{xx},\ 0<x<1,\ t>0; \ u(x,0)=0,$ and $-u_x(0,t)=u_x(1,t)=\phi(t),$ where $\phi(t)$ is a control function that ensures that the total mass $\int_0^1 u(x,t_k)dx$ stays between two predetermined…