Modal And Diffusion Characterization Of K+Na+ Exchanged Glass Waveguides

Najafi, S. Iraj; Lapierre, Jean‐François; Maciejko, R.; Seguin, F.; Champagne, A.; Blaha, F.

doi:10.1117/12.967392

Cited by 5 publications

(6 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the numerical calculations in [28] it was argued that not only the crystal configurations but also some configurations that although not perfectly crystal but very close to that can also flow to a boundary conformal field theory. This fact will be important in our later discussion regarding the localizble entanglement [37]. Finally, it is worth mentioning that all of the above results are valid when we are making the measurement in the σ z basis.…”

Section: Conformal Configurationsmentioning

confidence: 60%

“…In these particular circumstances interestingly one can even go further and calculate the probability of occurrence of particular configuration as the result of the projective measurement [27,28,29]. We will come back to this point when we discuss localizable entanglement [37]. In the following sections we will first summarize the results of [21] and [30] for the infinite and the periodic systems.…”

Section: Conformal Field Theory Results: 1+1 Dimensionsmentioning

confidence: 99%

“…Consequently knowing p i in our setup can in principle provide a lower-bound for the localizable entanglement. A complete discussion about this point will appear in a future work [37]. Finally note that, as we will discuss in more detail in section 11, in our setup we do not consider the evolution of the entanglement entropy after selective measurement as it is discussed in [35].…”

Section: )mentioning

confidence: 99%

See 2 more Smart Citations

Entanglement entropy after selective measurements in quantum chains

Najafi

Rajabpour

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

We study bipartite post measurement entanglement entropy after selective measurements in quantum chains. We first study the quantity for the critical systems that can be described by conformal field theories. We find a connection between post measurement entanglement entropy and the Casimir energy of floating objects. Then we provide formulas for the post measurement entanglement entropy for open and finite temperature systems. We also comment on the Affleck-Ludwig boundary entropy in the context of the post measurement entanglement entropy. Finally, we also provide some formulas regarding modular hamiltonians and entanglement spectrum in the after measurement systems. After through discussion regarding CFT systems we also provide some predictions regarding massive field theories. We then discuss a generic method to calculate the post measurement entanglement entropy in the free fermion systems. Using the method we study the post measurement entanglement entropy in the XY spin chain. We check numerically the CFT and the massive field theory results in the transverse field Ising chain and the XX model. In particular, we study the post meaurement entanglement entropy in the infinite, periodic and open critical transverse field Ising chain and the critical XX model. The effect of the temperature and the gap is also discussed in these models.Comment: Published version: 71 pages, 36 figures. added new references

show abstract

Section: Conformal Configurationsmentioning

confidence: 60%

Section: Conformal Field Theory Results: 1+1 Dimensionsmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

See 1 more Smart Citation

Entanglement entropy after selective measurements in quantum chains

Najafi

Rajabpour

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…boundary counterparts see [5,33]. The corresponding annulus partition functions of different boundary conditions are listed in Appendix B.…”

Section: Transverse Field Ising Chain: Numerical Calculationsmentioning

confidence: 99%

Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories

Rajabpour¹

2016

J. Stat. Mech.

View full text Add to dashboard Cite

We calculate formation probabilities of the ground state of the finite size quantum critical chains using conformal field theory (CFT) techniques. In particular, we calculate the formation probability of one interval in the finite open chain and also formation probability of two disjoint intervals in a finite periodic system. The presented formulas can be also interpreted as the Casimir energy of needles in particular geometries. We numerically check the validity of the exact CFT results in the case of the transverse field Ising chain.

show abstract

“…Load is applied to test such structures by mechanical, dynamic and electrostatic methods. These methods include a resonant frequency technique on cantilever beam test structures or capacitive micromachined ultrasonic transducer membranes [6][7][8]; a direct tensile stress technique [9][10][11]; a capacitance/voltage technique on fixed-fixed beam bridge structures or differential capacitive strain sensors [12,13]; an electrostatic pull-in technique on tethered rigid parallel-plate structures [14][15][16]; a direct mechanical bending of cantilever beam test structures by a known force and measurement of the resulting deflection [17,18]; a load/ deflection technique on suspended thin film membranes/ plates under tensile stress and known pressure load [19][20][21], and which is extended by [22] using a surface profilometer or developed by [23] called the Balance method. Moreover, other approaches are adopted not only for Young's modulus but also for testing other mechanical properties.…”

Section: Introductionmentioning

confidence: 99%

A novel method for determining Young’s modulus of thin films by micro-strain gauges

Pan

2005

Microsystem Technologies

View full text Add to dashboard Cite

This work presents a novel method for in-situ determining Young's modulus of thin films at the wafer level by using a set of compact micromachined test structures and without any extra load applied to test such structures. The test structures comprise of a pair of microstrain gauges with known Young's modulus and a cantilever beam made of the measured film. The method utilizes inexpensive and available optical measuring equipment. An analytical model is derived to extract the Young's modulus of the measured film. A conventional surface-sacrificial layer micromachining technique is used to fabricate the structures. The micro strain gauges employed in the measurement are made of low-pressure chemical-vapor deposition (LPCVD) undoped polycrystalline silicon films produced by Semiconductor Research Center (SRC) and the measured film is made of PECVD silicon nitride for demonstration. The average value of the obtained Young's modulus of PECVD silicon nitride SiN x is 170 ± 3 GPa by using strain gauges with a residual stress of 211 ± 10 MPa.

show abstract

Modal And Diffusion Characterization Of K+Na+ Exchanged Glass Waveguides

Cited by 5 publications

References 0 publications

Entanglement entropy after selective measurements in quantum chains

Entanglement entropy after selective measurements in quantum chains

Finite size corrections to scaling of the formation probabilities and the Casimir effect in the conformal field theories

A novel method for determining Young’s modulus of thin films by micro-strain gauges

Contact Info

Product

Resources

About