To measure fluctuations on the zero-point level with our amplifier that adds more than 20 quanta of noise, we must average over many hours, or even days, to obtain acceptable levels of signal-to-noise. Even on these time scales, our system is very stable. We observe changes of less than 1% in the through power of our pump or probe tones, as shown in Fig. 4.12. The drift in through power we do see is most likely due to the frequency drift of our room-temperature filter cavities, as we know that their frequency is strongly temperature-dependent. Note that our measurement scheme should not be affected by system-wide changes in gain, as we always normalize the **mechanical** spectrum by the probe through power. Changing input gain can change the **squeezing** pump intra-cavity occupation, however, which could change the amount of **squeezing** in the mechanics. Frequency- dependent changes in input gain, like those from shifting filter cavities, can also change the probe power ratio, which can introduce errors into the measured spectra. We thus reset the filter cavities and adjust pump powers twice a day to prevent large-scale drifts.

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The Heisenberg uncertainty principle, or the standard **quantum** limit [1,2], imposes an intrinsic limitation on the ultimate sensitivity of **quantum** measurement sys- tems, such as atomic forces [3], infinitesimal displace- ment [4], and gravitational-wave [5] detections. When detecting very weak physical quantities, the **mechanical** **motion** of a nano-**resonator** or nanoelectromechanical system (NEMS) is comparable to the intrinsic fluctua- tions of the systems, including thermal and **quantum** fluctuations. Thermal fluctuation can be reduced by decreasing the temperature to a few mK, while **quantum** fluctuation, the **quantum** limit determined by Heisen- berg relation, is not directly dependent on the tempera- ture. **Quantum** **squeezing** is an efficient way to decrease the system **quantum** [6-8]. Thermomechanical noise **squeezing** has been studied by Rugar and Grutter [9], where the **resonator** **motion** in the fundamental mode was parametrically squeezed in one quadrature by peri- odically modulating the effective spring constant at twice its resonance frequency. Subsequently, Suh et al. [10] have successfully achieved parametric amplification and back-action noise **squeezing** using a qubit-coupled nanoresonator.

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Moreover, there is an overlooked technique: the resistive cooling ex- plored in the early experiments for gravitational wave detection 40 years ago [10]. A simple cold resistor was used to dissipate the thermal energy of a ton-scale **mechanical** **resonator**, and the resistor could also be artificially cold [11]. Unfortunately, they have been rarely studied ever since. We are attracted by the simplicity of this approach, and in this thesis, we study the resistive cooling with an artificial cold resistor (ACR), looking for possibil- ities to cool a miniature **mechanical** **resonator**. Although it would not be a candidate for ground state cooling, it might be an important tool resolv- ing experimental challenges. Particularly, opening an electrical access to control the **motion** of an “massive” (compared to those reached **quantum** ground state) optomechanical **resonator**, would be very interesting for the yet-challenging ground-state cooling experiments. A practical example is discussed in Chapter 4.

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We have shown that it is possible to generate continuous-variable cluster states on electromagnetic cavity modes by choosing a suitable relativistic **motion** of the cavity. The entanglement grows linearly in time. The size of the lattice is determined by the choice of initial driving frequency, the amount of entanglement required between every mode and the desired length-to-height ratio of the square cluster. As a first experimental implementation, we propose a simple example of a four-mode square cluster state in a superconducting **resonator** with tuneable boundary con- ditions. This scheme is within reach of current circuit QED technology and would be the first demonstration of a multipartite continuous variable cluster state in cQED. An interesting avenue of research would be the extension to regimes of high **squeezing** levels, such as the ones required for fault-tolerant **quantum** computing with CV cluster states 37 . In brief, our main contribution is to implement cluster states in relativistic **quantum** field theory, paving

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We have shown that it is possible to generate continuous-variable cluster states on electromagnetic cavity modes by choosing a suitable relativistic **motion** of the cavity. he entanglement grows linearly in time. he size of the lattice is determined by the choice of initial driving frequency, the amount of entanglement required between every mode and the desired length-to-height ratio of the square cluster. As a irst experimental implementation, we propose a simple example of a four-mode square cluster state in a superconducting **resonator** with tuneable boundary con- ditions. his scheme is within reach of current circuit QED technology and would be the irst demonstration of a multipartite continuous variable cluster state in cQED. An interesting avenue of research would be the extension to regimes of high **squeezing** levels, such as the ones required for fault-tolerant **quantum** computing with CV cluster states 37 . In brief, our main contribution is to implement cluster states in relativistic **quantum** ield theory, paving

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In the measurements of this work, the same optical laser beam used to cool the **mechanical** oscillator is also used to detect its **mechanical** **motion**. Photodetection of the transmitted cooling beam and the light scattered by the **mechanical** oscillator produce a heterodyne output signal proportional to the **mechanical** **motion**. This also means that fluctuations in the cooling laser beam input that are imprinted into the **mechanical** system, are also read out by a beam containing the same fluctuations. In addition to potentially raising the phonon number beyond the **quantum**-backaction limit (in the case of added technical laser noise beyond shot noise), noise on the input cooling beam can also lead to a coherent cancellation effect at the readout called “noise squashing” which may cause the **mechanical** mode occupation to be inferred incorrectly (note that this effect can also be understood in terms of the recently demonstrated electromagnetically induced transparency (EIT), whereby noise photons are transmitted and/or reflected through a transparency window created by the cooling beam). Noise squashing has been studied in low-frequency **mechanical** systems, where excess laser phase noise can be an issue, and in recent microwave work where the electromagnetic cavity is populated with residual photons [49].

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30 nm) versus wavelength are plotted in Figure 7a according to Equation 3. The α value of each longitu- dinal mode of GNR with different ARs (4 to 8) is also plotted for comparison. The results show that these modes of GNR exhibit a correlation to the dispersion re- lation of GNW. In addition, the decay length ð 1=k 00 Þ of GNW and the apparent **quantum** yield, η ¼ P r = ð P r þ P nr Þ,

Inconsistencies of some standard **quantum** **mechanical** models (Madelung’s, de Broglie’s models) are eliminated as- suming the micro particle movements on continuous, but non-differentiable curves (fractal curves). This hypothesis, named by us the fractal approximation of **motion**, will allow an unitary approach of the phenomena in **quantum** me- chanics (separation of the physical **motion** of objects in wave and particle components depending on the scale of resolu- tion, correlated motions of the wave and particle, i.e. wave-particle duality, the mechanisms of duality, by means of both phase wave-particle coherence and wave-particle incoherence, the particle as a clock, particle incorporation into the wave and the implications of such a process). Moreover, correspondences with standard gravitational models (Ein- stein’s model, string theory) can be also distinguished.

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stabilize a desired working regime of a discussed object is constructed in such a way that all resources of the control are used for suppressing unstable modes of **motion**. Such method of control law design provides maximal basin of attraction of the desired working regime. Problems of both local and global stabilization are investigated in the paper. When solving global stabilization problems, it is necessary to construct essentially nonlinear control functions. Optimal control and optimal trajectories are designed for some problems. The time-optimal control is designed using Pontryagin maximum principle. The optimal control is obtained in form of feedback. In some cases, intuitive consideration is used to create a control law.

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In previous experiments the acoustic presence of DPOAEs recorded from the locust ear suggested that the organ possesses non-linear hearing derived from active and **mechanical** non-linearities (Kössl and Boyan, 1998; Möckel et al., 2007). Complex sound processing in the locust ear has been known for some time; it is one of the few insect auditory organs known to be capable of frequency discrimination and having specific groups of cells for particular frequency ranges (Gray, 1960; Michelsen, 1971a). Regardless of this, the organ was previously considered to be a linear system (Breckow and Sippel, 1985; Michelsen, 1971b; Michelsen, 1971c). It was thought that all insect tympanal organs functioned passively through the **mechanical** **motion** of the membrane as no non-linear

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We organize the rest of this paper as follows. In section 2, the initial spin coherent state is introduced and its uncertainty aspects are discussed. Then, its time evolution via Hamiltonian (1) is considered and time dependent spin operators are obtained. Time depen- dence of the **squeezing** parameters (2) and (3) are also discussed in section 2. In section 3, entanglement parameters, their time dependence and their relationship to the **squeezing** parameters, are considered. Finally, section 4 is devoted to discussion and conclusions.

variables” and “**quantum** stochastic processes”. The usual theory of such processes was established in a well-known paper by Accardi, Frigerio and Lewis ([1]). At its heart is the notion of a **quantum** random variable as an algebra homomorphism from a “state space algebra” into a “probability space algebra.” This generalises the fact that every classical random variable X defined on a probability space (Ω, F, P ) and taking values in a measurable space (U, U ) gives rise to a homomorphism j from the algebra B b (U) of

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On the other hand, recall that particular favor has paid on wave **quantum** mechanics; we have been intoxicated and paralyzed by the aura of **quantum** mechanics. Is the superconducting that make us wake up, let us see clearly the limitation of the traditional **quantum** mechanics. It make us to rethink why can the Bohr atomic model explain the hydrogen spectral series accurately to be regarded as a wrong thing at starting point, complain why we have to temporarily abandon the description of pure wave **quantum** mechanics for explaining the general dispersion force between all of molecules, worry the unsolved physical mechanism of the formation of light polarizability and the elliptic polarization, and look back the embarrassed issue we faced in electron spin. So, if a direct answer must be given, it seems that, as to the explanation of uncertainty relation, Heisenberg was right, and Earl Kennard would be wrong.

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Mesoscopic magnetic systems in ferromagnets with a uniaxial magnetic anisotropy are nowadays the subject of considerable attention both theoretically and experimen- tally. Among these systems are distinguished, especially domain walls (DWs) and elements of its internal structure - vertical Bloch lines (BLs; boundaries between domain wall areas with an antiparallel orientation of magnetization) and Bloch points (BPs; intersection point of two BL parts) [1]. The vertical Bloch lines and BPs are stable nanoformation with characteristic size of approximately 10 2 nm and considered as an elemental base for magnetoelectronic and solid-state data-storage devices on the magnetic base with high performance (**mechanical** stability, radiation resistance, non-volatility) [2]. The magnetic structures similar to BLs and BPs are also present in nanostripes and cylindrical nanowires [3-6], which are perspective materials for spintronics.

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Now, all of the above time evolution equations for the reduced density operator may be equivalently treated using the Wigner-Moyal phase space representation of quantum me chanics, thus[r]

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So, in front of leakage **squeezing**, not only the attacker shall conduct an attack of much higher order, but also she will get a very degraded distinguisher value. On n = 4 bits, the optimal first-order leakage **squeezing** is linear and allows to reach resistance order of 3. The used optimal code is [8, 4, 4]. For the second-order leakage **squeezing**, we can resort to the linear code [12, 4, 6], that improves by two (6 − 4 = 2) orders (with only one additional mask) the resistance against HO- CPA. By the trivial construct of Sec. 3.4, only one additional order of resistance would have been gained. A summary of the results is shown in Tab. 2. The improvement from the “straightforward” to the “squeezed” masking is of two orders with one mask and three orders with two masks.

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ABSTRACT: The need for different applications leads to various kinds of filter designs and numerous scaling techniques are used. This paper illustrates the basic principle of working of Microelectromechanical **resonator** which is fundamental part of filter. This **resonator** can be used in oscillator and filter. This paper also includes the results from the simulation of clamped free beam **resonator** in COMSOL multiphysics.

The elucidation of the mechanism on the biological effects of weak chemical and physical factors on cells and organism is one of the modern problems in life sciences. According to the Receptor Theory of Prof. Bernard Katz the im- pact of the biological substances on cells is realized through the activation of ligand-gated ion channels in the membrane. However, this theory doesn’t provide a satisfactory explanation on the similar biological effects of extremely low concentrations of different chemical substances, which are unable to acti- vate the ionic channels in the membrane and have non-linear dose-dependent effect on cells. Previously we have suggested that the metabolic control of cell hydration serves as a universal **quantum**-**mechanical** sensor for different weak physical and chemical signals. For supporting this hypothesis, in this article the comparative study of the effects of low concentrations of both cold (non-radioactive) and [ 3 H]-ouabain (specific inhibitor for Na + /K + -ATPase) on

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